Introduction to Logic

Exercise 3.3 - Propositional Entailment

The truth table at the bottom of this page gives values for the three Propositional Logic sentences on the right for all possible values of the three proposition constants shown on the left.

p q r   pqr pr qr
1 1 1   1 1 1
1 1 0   1 0 0
1 0 1   1 1 1
1 0 0   0 0 1
0 1 1   1 1 1
0 1 0   1 1 0
0 0 1   1 1 1
0 0 0   1 1 1

Use this truth table to answer the following questions about logical entailment.

a. {pqr} ⊨ (pr)
b. {pr} ⊨ (pqr)
c. {qr} ⊨ (pqr)
d. {pqr, pr} ⊨ (qr)
e. {pqr, qr} ⊨ (pr)