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!”.

Explain.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**.All logical combinations can be made using only

**nand**. For instance \[\text{not } = A\text{ nand }A.\] Please show that this formula is correct.Write the formula for

**and**using only**nand**Write the formula for

**or**using only**nand**(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?