Help with this please. I have to form the contrapositive of each and simplify negation using DeMorgan's rules.
a) a->(b or c)
my answer:
contra(~b or~c)->~a
simplified: ~b and ~c->~a
b) (A and B)->(~q)
my answer:
contra (~A or~b)->q
simplified:~a or ~b->q
Am i even close?
For part a):
To form the contrapositive, you need to switch the positions of the antecedent (a) and consequent (b or c) while also negating both. So the contrapositive of "a -> (b or c)" would be "~(b or c) -> ~a".
To simplify the negation using DeMorgan's rules, you distribute the negation over the disjunction (b or c). That means you change "~(b or c)" to "~b and ~c". Therefore, the simplified form of the contrapositive is "~b and ~c -> ~a".
Your answer of "~b and ~c -> ~a" is correct for part a).
For part b):
To form the contrapositive, you again switch the positions of the antecedent (A and B) and the consequent (~q) while negating both. So the contrapositive of "(A and B) -> (~q)" would be "~(~q) -> ~(A and B)".
To simplify the negation using DeMorgan's rules, you change "~(~q)" to "q" and "~(A and B)" to "~A or ~B". Therefore, the simplified form of the contrapositive is "q -> ~A or ~B".
Your answer of "q -> ~A or ~B" is correct for part b).
So, overall, you are indeed close, as your answers for both parts are correct.