1. Construct a truth table for each proposition.

(a) [(p q) r] [(p r) (q r)]

(b) [(p r) (q r)] [(p q) r)]

2. Let U := Letters in the English Alphabet = {a, b, c, . . . ,x, y, z}

A = {t, r, i, a, n, g, l, e, s}

B = {s, q, u, a, r, e };

C = {h, e, x, a, g, o, n, s }

Determine the following:

(a) A (B C)

(b) (A B) 0 C

(c) (A C) (B C)

(d) A (C U )

(e) n[(A B) ( B C )]

3. A survey of 90 customers was taken at Barnes & Noble regarding the types of books purchased. The survey found that 44 purchased mysteries, 33 purchased science fiction, 29 purchased romance novels, 13 purchased mysteries and science fiction, 5 purchased science fiction and romance novels, 11 purchased mysteries and romance novels, and 2 purchased all three types of books (mysteries, science fiction, romance novels). How many of the customers surveyed purchased

(a) mysteries only?

(b) mysteries and science fiction, but not romance novels?

(c) mysteries or science fiction?

(d) romance novels or mysteries, but not science fiction?

(e) exactly two types (mysteries, science fiction, romance novels)?

4. Use Polya's Four Steps to solve the following problems.

(a) Susie's age this year is a multiple of 5. Next year, her age is a multiple of 7. What is her present age?

(b) Consider a square whose side is 1 unit. If the measure of its side is doubled, what will be its new area as compare to the smaller square? How about if the side of the smaller square was tripled, what will be its new area?

(c) How many perfect squares are there between 1,000,000 and 9,000,000?

(d) Determine the number of different triangles that can be drawn given eight noncollinear points?

(e) There are 25 students asked by their literature instructor regarding with the type of literary works they prefer to read. He found out that 10 prefer to read novels, 11 prefer to read short stories, 15 prefer to read poems, 5 for both novels and short stories, 4 both short stories and poems, 7 for both novels and poems, and 3 prefer all. How many students prefer none of the given types of literary works?