A. By using the truth table (Truth matrix), show that each statement is a tautology, contradictory or
a contingent statement.
1. ¬p ^ q
p
1
0
1
0
¬p ^ q is a contingency
¬p
0
1
0
1
q
0
1
1
0
¬p^q
0
1
0
0
2. ¬(p v q)q
p
q
1
0
0
1
0
0
1
1
¬(p v q)q is a contingency
pvq
1
1
0
1
¬(p v q)
0
0
1
0
¬(p v q)q
1
1
0
1
3. ¬(¬p ^ q) v q
p
q
1
0
0
1
1
1
0
0
¬(¬p^q) v q is a tautology
¬p
0
1
0
1
¬p^q
0
1
0
0
¬(¬p^q)
1
0
1
1
¬(¬p^q) v q
1
1
1
1
4. ¬p(pq)
p
q
1
0
0
1
1
1
0
0
¬p(pq) is a tautology
¬p
0
1
0
1
(pq)
0
1
1
1
¬p(pq)
1
1
1
1
pvq
1
1
1
0
¬q(p v q)
1
1
1
0
5. ¬q(p v q)
p
q
1
0
0
1
1
1
0
0
¬q(p v q) is a contingency
¬q
1
0
0
1