HOUSTON — Former HUD Secretary Julian Castro questioned Thursday whether former Vice President Joseph R. Biden has struggled with some memory lapses in the third presidential debate.

When Mr. Biden said that people would not have to buy into his health care plan, Mr. Castro pounced.

“You said two minutes ago that they would have to buy in,” Mr. Castro said. “Are you forgetting what you said two minutes ago?”

The crowd responded with moans and murmurs.

“Are you forgetting already what you said two minutes ago?” he said. “I can’t believe that you said two minutes ago that they had to buy in, and now you are saying they don’t have to buy in. You are forgetting that.”

Mr. Biden rejected Mr. Castro’s claim.

“I am fulfilling the legacy of Barack Obama and you are not,” Mr. Castro said.

Mr. Biden shot back, “that would be a surprise to him.”

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