Question

Construct a truth table for each of the following compound statements, where p, q, r. denote primitive statements.

a. ∼ ( p ⌄ ∼ q ) → ∼ p
b. p → ( q → r )
c. ( p → q ) → r
d. ( p → q ) → ( p ^ q)​

Answer 1

See below for solution

When I post this I lose the formatting but you should be able to figure it out

Explanation:

Part a

p q ∼ ( p ∨ ∼ q ) → ∼ p
------------------------------------------------------------

True True True

True False True

False True True

False False True

Part b

p q r p → ( q → r )
-----------------------------------------------------------------

True True True True

True True False False

True False True True

True False False True

False True True True

False True False True

False False True True

False False False True

Part c

p q r ( p → q ) → r
-----------------------------------------------------------

True True True True

True True False False

True False True True

True False False True

False True True True

False True False False

False False True True

False False False False

Part d

p q (p → q)→(p ∧ q)
---------------------------------------------------

True True True

True False True

False True False

False False False