a) [5 marks] Construct the truth tables of the statements

(p ? r) ? (r ? q) and p ? (q ? r).

Determine whether they are logically equivalent.

b) [51 marks] In the questions below suppose that the variable x represents people, F (x): x is friendly, T (x): x is tall and A (x): x is angry. Write each of the following statement using these predicates and any needed quantifier:

i. Some people are not angry.

ii. All tall people are friendly.

iii. No friendly people are angry.

iv. Some tall angry people are friendly.

v. If a person is friendly, then that person is not angry.