Blog of Andrés Aravena

Homework 8

30 April 2023. Deadline: Tuesday, 9 May, 15:00. by Andrés Aravena, Ph.D.
  1. Three philosophers enter in a bar.
    The bartender asks “Will all of you drink beer?”.
    The first says “I don’t know”
    The second says “I don’t know”.
    The third says “Yes!”.

  2. In digital electronics, one of the easiest logic gates is called nand, and it represents the combination not and. In other words \[A\text{ nand }B= \text{not }(A\text{ and }B).\] Please write the truth table for nand.

  3. All logical combinations can be made using only nand. For instance \[\text{not } = A\text{ nand }A.\] Please show that this formula is correct.

  4. Write the formula for and using only nand

  5. Write the formula for or using only nand

  6. (Bonus) To prove that \(\sqrt{2}\) is not a fraction, we used the hypothesis that “if \(p^2\) is even (i.e. \(p^2=2r\) for some integer \(r\)) then it must be true that \(p\) is even”. Can you suggest an idea of how this hypothesis could be proved to be true?

Deadline: Tuesday, 9 May, 15:00.

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