Simple Proofs

Prove the following (show your work): If a is odd, b is odd, and c even then a b c is even

Prove the following (show your work): If a is divisible by 2 and b is divisible by 5 then a b is divisible by 10.

Quantified Logic

Convert the following statement to a quantified expression, negate it, and convert the answer back to English. You will end up with the exact opposite concept.

All cats are asleep.

Convert the following statement into a quantified expression:

Everyone, who has seen Deadpool, likes chimichangas .

Simplify the following Quantified Statement. The result should have no negation symbols.

?x ?x (G(x) ? H(x) )

Induction

4. Prove the following using induction (show your work- both steps):

Ifx?2then2+4+6+...+2n = n(n+1)