Question

Define Tautology and Contradiction. Construct the truth table for the compound statement(~ ∧ ( ∨ )) ⇒∼ (∼ ). What would you conclude from the truth table?​


(please solve that)

Answer 1

A compound proposition that is always true for all possible truth values of the propositions is called a tautology. A compound proposition that is always false is called a contradiction. A proposition that is neither a tautology nor contradiction is called a contingency. Example: p ∨ ¬p is a tautology.

hint

Answer

The given statement pattern is

(p∧∼q)↔(p→q)

Truth Table

p q ∼q p∧∼q p→q (p∧∼q)↔(p→q)

T T F F T F

T F T T F F

F T F F T F

F F T F T F

All the entries in the last column of the above truth table are F.

∴(p∧∼q)↔(p→q) is a contradiction