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Using the truth table, verify p → (p → q) ≡ ~ q → (p → q)

EXERCISE 1.6Q 6.2   PAGE 16
Exercise 1.6 | Q 6.2 | Page 16

Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


SOLUTION

123456
pq~qp→qp→(p→q)~q→(p→q)
TTFTTT
TFTFFF
FTFTTT
FFTTTT

In the above truth table, entries in columns 5 and 6 are identical.

∴ p → (p → q) ≡ ~ q → (p → q)