Question

Write an equivalent sentence for the statement. It is false that cats are lazy or dogs are not friendly. (Hint: Use De Morgan's laws.)

A. Cats are not lazy or dogs are not friendly.

B. Cats are not lazy and dogs are friendly.

C. Cats are lazy and dogs are friendly.

D. Cats are not lazy or dogs are friendly.

Answer 1

\[\sim(A\vee B) = (\sim A)\wedge(\sim B)\] is the one we need...

so A = cats are lazy,
B= dogs are not friendly

~A = cats are not lazy
~B = dogs are friendly

since the proposition includes an "or" you need to change it to an "and" and negate each part.

thus ~A "and" ~B