Tautologies

A wff whose truth values are always true, is called a ________

A tautology is ______ _______ by its very structure

"Today the sun will shine or today the sun will not shine" is called a Tautology

The following statement is a tautology

A ∨ A'

A wff whose truth values are always false, is called a _______

A contradiction is _____ ______ by its very structure

Mark the following statements as tautology or contradiction

“Today is Tuesday and today is not Tuesday” is a contradiction

Equivalent wffs

Suppose that P ↔ Q is a tautology and truth table for all letters in both statements agree for every row.  In this case P and Q are said to be equivalent wffs, denoted by

Is the following an equivalent wffs?

(A → B) ⇔ (B' → A')

Some Tautological Equivalences

Assign the right properties to the rows

A ∨ B ⇔ B ∨ A	A ∧ B ⇔ B ∧ A	(1)
(A ∨ B) ∨ C ⇔ A ∨ (B ∨ C)	(A ∧ B) ∧ C ⇔ A ∧ (B ∧ C)	(2)
A ∨ (B ∧ C) ⇔ (A ∨ B) ∧ (A ∨ C)	A ∧ (B ∨ C) ⇔ (A ∧ B) ∨ (A ∧ C)	(3)
A ∨ 0 ⇔ A	A ∧ 1 ⇔ A	(4)
A ∨ A' ⇔ 1	A ∧ A' ⇔ 0	(5)