FLAUM, Circuit Judge.

Jeffory Schane, now retired, receives a monthly pension from his union pension plan. The plan's board of trustees has determined that, based on its interpretation of the pension plan, Schane is entitled to $2,600 per month. Schane reads the plan differently, and believes he should receive $2,900. We are asked to decide whether the trustees' interpretation of the plan is arbitrary or capricious.

I. Background

In February 2008, Jeffory Schane suffered a job-related injury while working for YRC Roadway Express, a trucking company. He drew workers' compensation benefits until he returned to work in April 2009. Schane was medically cleared for light-duty work only, however, and with no work of that kind available, he resumed workers' compensation in March 2010. He continued taking workers' compensation benefits until he resigned from YRC on December 30, 2011.

YRC and its employees, including Schane, participate in the International Brotherhood of Teamsters Union Local No. 710 Pension Fund Pension Plan, a multi-employer benefit trust fund and an "employee pension benefit plan" within the meaning of 29 U.S.C. § 1002(2). Schane initially submitted a pension application to the plan in July 2009, after returning from his first stint on workers' compensation. However, he left blank the line on the application indicating his last day of work, apparently because the plan does not permit participants to take a pension while they are also receiving workers' compensation from their employer. See Summary Plan Description 4. The following March, Schane told the plan that his last day of work would be October 31, 2010. Three months later, he delayed his last day by a year, to October 31, 2011. In September 2011, he told the plan that he would no longer retire on October 31, 2011, either. Finally, on December 21, he wrote that he would retire at the end of the month and that his pension should therefore be effective on January 1, 2012. Schane resigned from YRC on December 30.

The Local No. 710 pension plan enumerates ten or so different pension categories, each with its own rules for calculating benefits. For present purposes we focus only on the "special regular pension," for which Schane is eligible. Benefits in the special regular pension are essentially a function of two variables: the number of "future pension credits" the pensioner has accumulated and the pensioner's age at the time of retirement.

Over Schane's years of service at YRC, the company made pension contributions on his behalf. These contributions, which totaled 25.6 credits, ceased in August 2009; YRC's agreement with the union only obligated it to make payments for a limited period while the employee was on workers' compensation. Once YRC's obligation was discharged, Schane made additional self-pay contributions (worth 0.4 credits) between August and December 2009 to bring the total up to 26 credits.

Section 3.062(b)(i) of the pension plan provides that a participant who retires with 26 credits is entitled to $2,600 per month. But a participant who retires "on or after age 50" with "26 or more but less than 27" future pension credits is entitled to $2,900 per month. Plan § 3.062(b)(ii). Schane's age at the time of retirement is thus a significant question, to the tune of $3,600 per year. However, Schane and the plan cannot agree on the date that he "retired" for plan purposes. The plan's board of trustees says August 2009; Schane says December 2011.

The plan defines "retirement," though not in an especially transparent way. An initial complication is that the term means different things depending on whether the pensioner has reached "Normal Retirement Age." (Per section 1.19 of the plan, normal retirement age occurs when an employee turns sixty-five or accumulates ten years of service, whichever is later.) The parties agree that Schane retired before normal retirement age, so only that portion of the "retirement" definition is relevant. For completeness, however, we reproduce the second part of the definition in a footnote.

Section 6.05: Retirement or Retires

Two terms in this definition require definition themselves. The first is "Covered Employment," which means employment with an employer who makes contributions to the pension fund on the employee's behalf. Plan § 1.09(b). The second is "Contributing Employer." Although this term is capitalized as if it were a specially defined term, it is not listed in the definitions section of the plan. But plain "Employer" is — in somewhat circular fashion, it means "any association or individual Employer" that must contribute to the trust fund pursuant to a collective bargaining agreement, or "any Employer not a party" to such an agreement but who assents to the trustees' satisfaction to be bound. Plan § 1.12. We take it therefore that "Contributing Employer" means an employer who contributes to the pension fund for some employees, but not for the particular employee in question.

In short, to use the plan's language, Schane was employed in Covered Employment until August 2009, when YRC ceased making contributions on his behalf. See Plan § 6.05(a). And Schane was engaged in employment with a Contributing Employer (namely, YRC) until December 2011, when he stopped receiving workers' compensation benefits and resigned from the company. See Plan § 6.05(a)(i).

After Schane submitted his final pension application, the board of trustees approved him for the lower pension of $2,600 per month. Schane appealed to a special committee of the trustees, arguing that although he ceased engaging in Covered Employment in August 2009, when he was forty-eight years old, his "retirement" did not occur until he also ceased employment with YRC in December 2011, at fifty. However, the committee upheld the trustees' initial determination. It reasoned:

Schane then filed an action in federal district court under ERISA. Schane argued that the trustees erred by focusing only on whether he had ceased working for a covered employer, while ignoring whether — and when — he had also ceased engaging in the activities precluded by section 6.05(a)(i)-(v). The district court too rejected Schane's argument. It observed that the plan's definition of "retirement" was phrased in the disjunctive: "`Retirement'... means cessation of being employed in Covered Employment or engaging in any of the following...." Plan § 6.05(a) (emphasis added). Furthermore, as the court noted, citing the Sixth Circuit's opinion in Marquette General Hospital v. Goodman Forest Industries, 315 F.3d 629, 633 (2003), "the word or does not also mean and." In light of this disjunctive definition, the district court concluded, the trustees appropriately interpreted section 6.05 to require either cessation of covered employment or cessation of the later-enumerated activities — not both. It awarded summary judgment to the defendants.

II. Discussion

The plan gives the board of trustees discretionary authority to construe its terms and determine eligibility for benefits. Therefore, like the district court, we review the trustees' reasoning only under an arbitrary and capricious standard. Tompkins v. Cent. Laborers' Pension Fund, 712 F.3d 995, 999 (7th Cir.2013). This generous standard requires us to uphold a fiduciary's interpretation of plan documents so long as it "has rational support in the record," Speciale v. Blue Cross & Blue Shield Ass'n, 538 F.3d 615, 621 (7th Cir.2008), but we are not a "rubber stamp." Cerentano v. UMWA Health & Ret. Funds, 735 F.3d 976, 981 (7th Cir. 2013).

The present dispute boils down to whether cessation of covered employment is sufficient for retirement or merely one of two necessary requirements (the other being cessation of the enumerated activities in section 6.05(a)(i)-(v)). The district court reasoned that, because the definition of "retire" took the form cessation of X or Y, the trustees were free to interpret it disjunctively: that is, to treat cessation of X as a sufficient condition. We find that the matter is not so clear.

Often, the word or does function as a straightforward disjunctive. Consider the following sentence: "parent" means someone who has a son or daughter. No one would contend that a man who has a daughter is not a "parent" because he does not also have a son. Clearly, to satisfy this definition, the man must only have a son or have a daughter; he does not need both. In this sentence, the word or indicates precisely what the board of trustees thought it did in section 6.05.

But consider another sentence, very similar to the previous one: "non-parent" means someone who does not have a son or daughter. Suppose the same man comes to you and claims he is a non-parent. True, he admits, he does have a daughter. However, he is quite certain that he does not have a son. The man notes that the definition of "non-parent" consists of two parts joined with an or, and furthermore that "the word or does not also mean and." Marquette, 315 F.3d at 633. Thus, he reasons, the definition is disjunctive; because he satisfies the first part of the definition (no son), it simply does not matter whether he satisfies the second (no daughter). QED.

The flaw in the man's argument is easy to spot. To be a non-parent, a person must not have a son or daughter — which is to say, he must not have a son and he must not have a daughter. Because this man does not satisfy the second part of the definition (he has a daughter), he is not a nonparent, even though he satisfies the first (he has no son).

Note how, in the paragraph above, the or-statement ("not have a son or daughter") was rephrased using only an and ("not have a son and not have a daughter"). This equivalence arises when a speaker combines a negation (like "not have") with a disjunctive word (like "or"). Another example from a recent book on legal interpretation illustrates the point: "After a negative, the conjunctive and is still conjunctive: Don't drink and drive. You can do either one, but you can't do them both. But with Don't drink or drive, you cannot do either one: Each possibility is negated." Antonin Scalia & Bryan A. Garner, Reading Law: The Interpretation of Legal Texts 119 (2012). In propositional logic, this move — the rule of inference that not (X or Y) is equivalent to not X and not Y — is known as one of "De Morgan's Laws." See Lawrence M. Solan, The Language of Judges 49 (1993). Formal notation aside, the point is merely that determining the meaning of or in a sentence is not just a matter of declaring that the word is disjunctive. Context matters.

Returning to the question at hand, is the cessation of covered employment sufficient to deem an employee retired? Put another way, is the definition of "retirement" in section 6.05(a) like the definition of "parent" or the definition of "non-parent" above? On its own, the answer is not obvious, in part because the plan's language — "cessation of being employed in Covered Employment or engaging in any of the following" activities — is so inelegant. Certainly the word "cessation" has the flavor of a negation; but given the unwieldy phrasing there may be room for debate.

In most cases, ambiguity would suggest that the interpretive question is for the trustees to decide. See Hess v. Reg-Ellen Machine Tool Corp., 423 F.3d 653, 662 (7th Cir.2005) ("The requirement that we give deference to the plan administrator's interpretation is especially applicable when plan language is ambiguous, for that is precisely when the administrator exercises his grant of discretion."). In this case, though, the trustees seem scarcely to have noticed the ambiguity in the first place.

Here again, in relevant part, is the committee's reasoning on the issue of Schane's age at "retirement":

Even under the deferential standard of review applied to ERISA actions, this explanation is lacking. It begins by misstating the definition of "retirement" from section 6.05(a). "Retirement" most certainly does not mean the cessation of being employed in covered employment — it means the cessation of being employed in covered employment or engaging in the activities listed in section 6.05(a)(i)-(v). Not surprisingly, because the explanation omits the second half of the definition, the trustees never suggest why "cessation of being employed ... or engaging" should be read disjunctively, rather than as a conjunctive prohibition that applies to both sides of the or. In these circumstances, "there simply is no analysis or `reasoning' to which the Court may defer under the arbitrary and capricious standard." Gritzer v. CBS, Inc., 275 F.3d 291, 296 (3d Cir.2002); cf. Trs. of Cent. States, Se. & Sw. Areas Health & Welfare Fund v. State Farm Mut. Auto. Ins., 17 F.3d 1081, 1083 (7th Cir.1994) ("Deferential review is appropriate only when the trust instrument allows the trustee to interpret the instrument and when the trustee has in fact interpreted the instrument." (emphasis added)).

Now, on appeal, the trustees do at least identify the issue. But their analysis is quite brief: "the subparts in the definition of retire are separated by the disjunctive word `or,'" they contend, "indicating that either subpart may constitute `retirement.'" Appellees' Br. 12. And although the trustees have substantial room to interpret ambiguous provisions, their interpretation still must be "compatible with the language and the structure of the plan document." Frye v. Thompson Steel Co., Inc., 657 F.3d 488, 493 (7th Cir.2011). We agree with Schane that the trustees' interpretation is untenable when viewed in the context of the rest of the plan. Schane makes a number of arguments to this end, but we will focus only on one: the argument that the trustees' interpretation cannot be reconciled with an accompanying plan provision that covers suspension of benefits.

The suspension-of-benefits section, section 6.06, requires a pensioner to notify the trustees if he is no longer "retired" within the meaning of section 6.05, and it permits the trustees to suspend an unretired pensioner's benefits until he once more enters retirement. Congress has specifically authorized benefits plans to include this sort of provision so that the plans are not used "to subsidize low-wage employers who hire plan retirees to compete with, and undercut the wages and working conditions of employees covered by the plan." Cent. Laborers' Pension Fund v. Heinz, 541 U.S. 739, 742 n. 1, 124 S.Ct. 2230, 159 L.Ed.2d 46 (2004) (citation omitted).

In the trustees' view, the fact that an employee has ceased covered employment is itself sufficient to deem that employee retired. This would undercut the suspension-of-benefits provision because a pensioner who resumed work in the same industry and geographic area would nevertheless remain retired. Why? Even though the employee would have resumed employment in one of the activities listed in section 6.05(a)(i)-(v) — and so would not satisfy the second half of the definition of "retirement" — the employee would still continue the "cessation of being employed in Covered Employment" (at least so long as the new employer did not make pension contributions on his behalf). Plan § 6.05(a). Under the trustees' interpretation, therefore, that employee would still be deemed "retired" despite now working for a competitor — largely vitiating the suspension-of-benefits clause.

The trustees' response to this argument is perplexing: "Assume, hypothetically, that in 2015, Appellant [i.e., Schane] wished to return to the same sort of work he performed for his employer prior to his retirement, but for a non-signatory employer." Appellees' Br. 17. "Under § 6.06," they write, "the Trustees would look at Appellant's proposed employment and could determine that his attempt to reenter employment in the same or related business as a Contributing Employer would therefore require suspension of his pension. Nothing in the determination made by the Trustees that Appellant retired in 2009 when contributions ceased being made on his behalf, precludes the Trustees from deciding at some point in the future whether or not Appellant has violated Section 6.05 and thus suspend his benefits." Id.

We do not see how this could be the case. Remember, the trustees have already argued that "the subparts in the definition of retire are separated by the disjunctive word `or,' indicating that either subpart may constitute `retirement.'" Id. at 12 (emphasis added). They cannot now turn around and say that, for suspension-of-benefits purposes, cessation of covered employment alone is not enough. The trustees elsewhere suggest that the word "retirement" should be understood differently in different contexts — that "under the clear terms of the plan, the definition of retirement has a different function depending on the circumstance." Id. at 15. But although the definition of "retirement" expressly distinguishes between retirement before and after normal retirement age, for example, see Plan §§ 6.05(a), (c), it says nothing about retirement for calculation-of-benefits purposes versus suspension-of-benefits purposes. "Once a term has been defined by the Plan and interpreted by the administrator to have a particular meaning, the administrator may not change the meaning when the term is used in a different part of the Plan without any basis in the Plan or in ERISA to do so." Reich v. Ladish Co., 306 F.3d 519, 525 (7th Cir.2002). To interpret the same defined term in two different ways in this manner is paradigmatically arbitrary and capricious. Id.

An ERISA plan "must be read as a whole, considering separate provisions in light of one another and in the context of the entire agreement." Schultz v. Aviall, Inc. Long Term Disability Plan, 670 F.3d 834, 838 (7th Cir.2012). Accordingly, we agree with Schane that, to the extent the plan's definition of "retirement" in section 6.05 is ambiguous, that ambiguity is resolved by looking to the accompanying suspension-of-benefits clause in section 6.06. In the context of the entire agreement, the only sensible interpretation of section 6.05(a) is that a participant must cease both covered employment and the activities listed in section 6.05(a)(i)-(v) to be deemed "retired."

When a plan administrator does not give adequate reasoning for its decision, we normally remand the case so that the administrator can make further findings or provide additional explanation. E.g., Holmstrom v. Metro. Life Ins. Co., 615 F.3d 758, 778 (7th Cir.2010); Love v. National City Corp. Welfare Benefits Plan, 574 F.3d 392, 398 (7th Cir.2009). But in light of the preceding discussion, and the trustees' flimsy defense of their own interpretation on appeal, we believe that it is "clear cut that it would be unreasonable for the plan administrator to deny the application for benefits on any ground." Id. (citing Gallo v. Amoco Corp., 102 F.3d 918, 923 (7th Cir.1996)). The judgment of the district court is REVERSED, and the case REMANDED for further proceedings consistent with this opinion.