Discrete mathematics

1. Let the universe be the set U = {0,1,2,3,4,5,6,7,8,9,10}. Let A = {0,1,4,7,10}, B = {0,1,2,3,4,5}, and C = {2,4,5,6,8}. List the elements of each set. (2 points each)

(a) B C

(b) A B

(c) A

(d) A B

(e)

2. What is the cardinality of {{a}, {a, b}, {a, c}, a, b, c}? (1 point)

3. Determine whether each pair of sets is equal. (1 point each)

(a) {x|x R and 0 < x 3}, {1, 2, 3}

(b) {2,1,1}, {1,2,2}

4. Let X = {1,2,3} and Y = {a,b,c,d}. List the elements in the set Y X. (2 points)

5. Answer true of false. (1 point each)

(a) {x} {x}

(b) {x} {x}

(c) {x} {x, {x}}

(d) {x} {x, {x}}

(e) {2} P({1,2})

(f) {2} P({1, 2})

6. List the members of P({a, b, c, d}). Which are proper subsets of {a, b, c, d}? (5 points)

7. Write the truth table of the proposition (p q) (q r). (5 points)