Let P be the compound proposition It is not the case that bo

Let P be the compound proposition \"It is not the case that both 12 lessthanorequalto x lessthanorequalto 20 and y is not even\". (a) Write P using symbolic notation. Define any other propositions that may be needed. (b) Simplify the symbolic notation using DeMorgan\'s Law and double negation. (c) Write the result from (b) using English.

Solution

a) Q: 12<=x<20

R: y is even

P: not(Q and not(R))

b) De Morgan\'s law : not(A and B) = not(A) or not(B)

Hence, P: not(Q) or not(not(R)) : not(Q) or R

c) It is not 12<=x<20 or y is even.