Section 1.2 #10. Show that each of these conditional statements is a tautology by using
truth tables.
(a) [¬p ∧ (p ∨ q)] → q
p
T
T
F
F
q
T
F
T
F
¬p
F
F
T
T
p∨q
T
T
T
F
¬p ∧ (p ∨ q)
F
F
T
F
[¬p ∧ (p ∨ q)] → q
T
T
T
T
(b) [(p → q) ∧ (q → r)] → (p → r)
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
p→q
T
T
F
F
T
T
T
T
q→r
T
F
T
T
T
F
T
T
(p → q) ∧ (q → r)
T
F
F
F
T
F
T
T
p→r
T
F
T
F
T
T
T
T
[(p → q) ∧ (q → r)] → (p → r)
T
T
T
T
T
T
T
T
(c) [p ∧ (p → q)] → q
p
T
T
F
F
q
T
F
T
F
p→q
T
F
T
T
p ∧ (p → q)
T
F
F
F
[p ∧ (p → q)] → q
T
T
T
T
(d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
p∨q
T
T
T
T
T
T
F
F
p→r
T
F
T
F
T
T
T
T
q→r
T
F
T
T
T
F
T
T
(p ∨ q) ∧ (p → r) ∧ (q → r)
T
F
T
F
T
F
F
F
[(p ∨ q) ∧ (p → r) ∧ (q → r)] → r
T
T
T
T
T
T
T
T