Question

1.Write the negation of the following statement in English. Do not simply add the words “not” or “it is not the case that” or similar before the existing statement. “Every dog likes some flavor of Brand XYZ dog food.”

2. Prove that the compound statements are logically equivalent by using the basic logical equivalences (13 rules). At each step, state which basic logical equivalence you are using. (p → q) ∧ (¬r → q) and (p ∨ ¬r) → q

Answer 1

1. The negation of the given statement is "At least one dog does not like a flavor of BRAND XYZ dog food".

2. The sign '=' will be used as equivalence between statements

Conditional rule

Distributive rule

Distributive rule

Distributive rule

The second statement (in the bracket) becomes q because when q is true the statement is true and when q is false it is false.

De Morgan's rule