1) Write truth tables for the statement forms in

A.p q

B. p (q r)

2) Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence.

1. p (p q) and p

2. p t and t

3. (p q) r and p (q r)

4. (p q) r and p (q r)

3) Assume x is a particular real number and use De Morgans laws to write negations for the statements

1. 2 < x < 7

2. x < 2 or x > 5

3. 1 > x 3

4) Use truth tables to establish which of the statement forms are tautologies and which are contradictions.

1. (p q) (p (p q))

2. (p q) (p q)

5) In the below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step.

(p q) (p q) p (q q) by (a)

p (q q) by (b)

p t by (c)

p by (d)

Therefore, (p q) (p q) p.

6) Use Theorem 2.1.1 to verify the logical equivalences in A and B. Supply a reason for each step.

1. (p q) p p

2. ((p q) (p q)) (p q) p