BENTON, Circuit Judge.

Remberto Aguinada-Lopez, a citizen of El Salvador, entered the United States illegally. He sought relief from removal by asserting claims for asylum, withholding of removal, and withholding under the Convention Against Torture. The Immigration Judge and Board of Immigration Appeals denied each claim. Having jurisdiction under 8 U.S.C. § 1252, this court denies the petition for review.1

Aguinada-Lopez is not a gang-member, but his cousin Oscar Gil belonged to the MS-13 gang (rival to the Dieciocho gang). Aguinada-Lopez alleges four incidents of violence in El Salvador. First, two men approached, asked if he were in a gang, and knocked him unconscious with a pistol. The second incident occurred when three men intercepted him, in his school uniform, leaving school (the National Industrial Technical Institute). The men beat him, threw rocks at him, bludgeoned him with sticks, and told him if he returned to the Institute, they would kill him. The third incident occurred when a man in black knocked him off his bicycle, pulled a gun, and said "You're that rat Oscar's cousin." When a car approached, the assailant fired three or four shots in the air and ran away. In the last incident, two men dressed in black shot at him. Aguinada-Lopez then went to stay at a friend's home, but members of the Dieciocho gang threatened his mother to "look for him anywhere, everywhere." Shortly after leaving El Salvador, members of the Dieciocho gang killed Oscar in front of Aguinada-Lopez's house as a "threat for [him] not to return...."

The Immigration Judge found Aguinada-Lopez credible but denied all claims for relief. The Board of Immigration Appeals affirmed. When the BIA adopts the decision of an IJ but adds additional reasoning, this court reviews both decisions. Setiadi v. Gonzales, 437 F.3d 710, 713 (8th Cir. 2006). Factual findings are reviewed for substantial evidence and not reversed unless "any reasonable adjudicator would be compelled to conclude to the contrary." 8 U.S.C. § 1252(b)(4)(B). Questions of law are reviewed de novo. Setiadi, 437 F.3d at 713.

I.

The Attorney General may not remove an alien to a country if it is determined "that the alien's life or freedom would be threatened in that country because of the alien's race, religion, nationality, membership in a particular social group, or political opinion." 8 U.S.C. § 1231(b)(3). An applicant for withholding based on membership in a particular social group must establish both a cognizable social group and a nexus between the persecution and membership in that social group. Gonzalez Cano v. Lynch, 809 F.3d 1056, 1058 (8th Cir. 2016).

Aguinada-Lopez claims persecution on account of his membership in two family-based social groups: (1) male, gang-aged family members of murdered gang members, and (2) male, gang-aged family members of his cousin Oscar. The Immigration Judge found the second "does constitute a particular social group under the Act." The BIA disagreed, finding that Aguinada-Lopez's "circumstances in this case are not meaningfully distinguishable from those in.... the Eighth Circuit's precedent decisions," and concluding that both proposed family-based social groups are not viable. See Antonio-Fuentes v. Holder, 764 F.3d 902, 905 (8th Cir. 2014) (rejecting a family-based social group — "member of a household" including cousin "killed by a gang"-because petitioner did not establish gangs specifically targeted his family as a group, thus no "different than any other Salvadoran family that has experienced gang violence"); Constanza v. Holder, 647 F.3d 749, 754 (8th Cir. 2011) (per curiam) (agreeing with BIA that "a family that experienced gang violence" (including harm to nephew and cousin) lacked visibility and particularity, thus "too broad to be perceived as social group[] by society."). The BIA also affirmed the IJ's finding that Aguinada-Lopez "did not establish a sufficient nexus ... based on his fear of gangs in El Salvador."

Assuming Aguinada-Lopez's proposed family-based groups are cognizable, this court affirms for failure to establish nexus. See Bernal-Rendon v. Gonzales, 419 F.3d 877, 881 (8th Cir. 2005) (recognizing that "a nuclear family can constitute a social group" and that the "prototype" and plainest example of a social group is "the immediate members of a certain family," but agreeing with the BIA that petitioners failed to prove a clear probability of a specific threat to their family as a social group (noting "extended family" still living without incident in Colombian cities)). Only the third incident is directly tied to his relationship to Oscar Gil. This single fact does not compel the conclusion that Aguinada-Lopez established nexus. See § 1252(b)(4)(B). The BIA did not err in denying withholding on the basis of the family-based particular social groups.

Aguinada-Lopez also claims persecution because of his membership in a third social group "male, gang-aged members of the Institute." He cites extensive evidence suggesting that students at the Institute are victimized by gangs. Although this may be sufficient to establish a cognizable social group, Aguinada-Lopez lacks evidence to prove nexus. The IJ found that the first, third, and fourth violent incidents were motivated by gang-recruitment, gang-membership, or his relationship to Oscar Gil. Attendance at the Institute may have motivated the second attack (when he was wearing his school uniform), but this single encounter does not, by itself, rise to the level of past persecution. See Eusebio v. Ashcroft, 361 F.3d 1088, 1091 (8th Cir. 2004).

The BIA did not err in denying Aguinada-Lopez's claim for withholding of removal.

II.

To qualify for relief under the Convention Against Torture, an alien must show "it is more likely than not that he or she would be tortured if removed to the proposed country of removal." 8 C.F.R. § 1208.16(c)(2). The torture must be inflicted "by or at the instigation of or with the consent or acquiescence of a public official or other person acting in an official capacity." § 1208.18(a). "Acquiescence" requires that the public official be aware of the activity and "thereafter breach his or her legal responsibility to intervene to prevent such activity." Id.

To show acquiescence, Aguinada-Lopez relies on country-conditions evidence identifying instances of police-corruption. However, these same documents also identify government efforts to end gang violence, including a stimulus program to rehabilitate gang members, a U.S.-funded wiretap center, and an elite anti-gang police unit. Certainly, El Salvador has struggled to protect against gang violence, but it has not acquiesced to gang violence. See Solis v. Mukasey, 515 F.3d 832, 836 (8th Cir. 2008) ("Although the government of El Salvador may struggle to control violence, there is no evidence in the record that government agents participate or acquiesce in possible torture perpetrated by others."); Mouawad v. Gonzales, 485 F.3d 405, 413 (8th Cir. 2007) ("A government does not acquiesce in the torture of its citizens merely because it is aware of torture but powerless to stop it...." (internal quotations and citation omitted)).

The BIA did not err in rejecting the CAT claim.2

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The petition for review is denied.