Use truth tables to determine if each of the following is a

Use truth tables to determine if each of the following is a tautology, a contradiction, or just satisfiable

d. p (p q)

e. p p q

f. (p q) (p q)

Solution

Given d. p (p q)

The given Expresssion  p (p q) is a  tautology.

Given e. p p q

The given Expression p p q is not satisfiable and it is not a tautology ,not a contradiction.

Given f. (p q) (p q) Here (p q) = (p NOR q) & (p q) = (p NAND q)

The given Expression (p q) (p q is not satisfiable and it is not a tautology ,not a contradiction.