Answer to Question #343794 in Discrete Mathematics for sabariah

Question

1. a) Determine whether the following proposition is logically equivalent or not using the truth table.

((p⟶q)v(q⟶p))⇔p⟷q

b) Construct a truth table to determine whether the following compound statement is a tautology, a contradiction or a contingency.

~(p∧r)⟶~(q∨r)

c) Use the laws of logic to establish the following logical expression.

~(p∨q) v (~p∧q)⟺~p

Answer 1

a.

Proposition is not logically equivalent.

b.

In the above truth table the entries in the last column are a combination of’ T ‘ and ‘ F ‘. So the given statement is neither propositions is neither tautology nor a contradiction. It is a contingency.

c.

De Morgan’s Laws:

¬(p ∨ q) ⇔ ¬p ∧ ¬q

¬qVq=T

Identity Law:p ∧ T ⇔ p

~(p∨q) v (~p∧q)=( ¬p ∧ ¬q)V (¬p ∧ q)=¬p∧(qV¬q)=¬p∧T=¬p