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I am trying to solve the following question with an example/proof. The question is from Introduction to Modern Cryptography by Katz and Lindell. Any help would be appreciated.

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Hints:

For (a), suppose you had a collision with $\hat{H}$; how could you use that to demonstrate a collision with $H$? What does that imply?

For (b), could you construct a collision with $\hat{H}$, that is, find two different messages $x_1||x_2$ and $x'_1||x'_2$ with $\hat{H}(x_1||x_2) = \hat{H}(x'_1||x'_2)$?

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