Midterm Quiz 2

Match the set identity that is used to justify each of the identities given below. 1) (B ∩ C) ∪ B ∩ C = U (there is a line over the second B C) 2) A ∪ (A ∩ B) = A (there is a line over all letters) 3) A ∪ (B ∩ C) = A ∪ (B ∪ C) ( one line over first B C, separate lines over second B and C) 4) (B - A) ∪ (B - A) = (B - A) 5) ((A ⊕ B) - C) ∩ ∅ = ∅ 6) (A ∪ B) ∩ C = (C ∩ A) ∪ (C ∩ B) 7) (A ∩ B) ∩ C = A ∩ (B ∩ C) = A ∩ B ∩ C

1) Complement law 2) Absorption law 3) De Morgan's law 4) Idempotent law 5) Domination Law 6) Distributive Law 7) Associative Law

Define the sets A, B, C, and D as follows: A = {-3, 0, 1, 4, 17} B = {-12, -5, 1, 4, 6} C = {x ∈ Z: x is odd} D = {x ∈ Z: x is positive} For each of the following set expressions, indicate whether the set is infinite or finite. 1) A ∪ B 2) A ∩ B 3) A ∩ C 4) A ∪ (B ∩ C) 5) A ∩ B ∩ C 6) A ∪ C 7) (A ∪ B) ∩ C 8) A ∪ (C ∩ D)

1) Finite 2)Finite 3)Finite 4)Finite 5)Finite 6)Infinite 7)Finite 8)Infinite

Indicate whether the statement is true or false. 1. Z ⊂ R 2. Z ⊆ R 3. Z ⊆ R+ 4. N ⊂ R 5. Z+ ⊂ N

1. True 2. True 3. False 4. True 5. True

What is the cardinality of the set { 0, 10, 20, 30, ...., 1000 } ?

101

What is the cardinality of the set { -3, -1, 1, 3, 5, 7, 9 } ?

7

Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }? a) { {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d} } b) { {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a}, {b}, {c}, {d} } c){ {a, b}, {a, c}, {a, d}, {b, a}, {b, c}, {b, d}, {c,a}, {c,b}, {c, d}, {a}, {b}, {c}, {d} } d){ {a, b}, {a, c}, {a, d}, {b, a}, {b, c}, {b, d}, {c,a}, {c,b}, {c, d} }

a) { {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d} }

A = {x ∈ Z : x is a prime number} B = {4, 7, 9, 11, 13, 14} C = {x ∈ Z: 3 ≤ x ≤ 10} Select the set corresponding to (A ∪ B) ∩ C. a) {3, 4, 5, 7, 9} b) {3, 5, 7} c) {3, 4, 7, 9} d) {3, 4, 5, 7, 9, 11, 13}

a) {3, 4, 5, 7, 9}

Use the definition below to select the statement that is false. A = {x ∈ Z: x is even and 4 < x < 17} a) |A| = 7 b) 4 ∉ A c) 6 ∈ A d) 17 ∉ A

a) |A| = 7

Select the set that is equivalent to C ∪ (C ∩ B). a) Ø b) C c) B ∩ C

b) C

Select the law that establishes that the two sets below are equal. (A ∩ B) ∪ (A ∩ B) = A ∩ B a) Identity law b) Idempotent law c) Distributive law d) Absorption law

b) Idempotent law

B = {x ∈ Z: x is a prime number} C = {3, 5, 9, 12, 15, 16} The universal set U is the set of all integers. Select the set corresponding to LaTeX: \overline{B}\cap C B ¯ ∩ C a) {3, 5, 9, 15} b) {9, 12, 15, 16} c) {9, 12, 16} d) {3, 5}

b) {9, 12, 15, 16}

Use the definitions below to select the statement that is true. A = {x ∈ Z: x is even} B = {x ∈ Z: −4 < x < 17} a) A ⊂ A b) Ø ⊂ B c) A is finite. d) B ⊆ A

b) Ø ⊂ B

What is the cardinality of the power set P({1, 2, 3, 4, 5, 6})? a) 6 b) 6^2 = 36 c) 2^6=64 d) 6*5*4*3*2*1=720

c) 2^6=64

Select the law that establishes that the two sets below are equal. LaTeX: A\cap\left(\overline{B\cup C}\right)=A\cap\left(\overline{B}\cap\overline{C}\right) a) Distributive law b) Absorption law c) De Morgan's law d) Associative law

c) De Morgan's law

C = {3, 5, 9, 12, 15, 16} D = {5, 7, 8, 12, 13, 15} Select the set corresponding to C ⊕ D. a) {3, 5, 7, 8, 9, 12, 13, 15, 16} b) {5, 12, 15} c) {3, 7, 8, 9, 13, 16} d) {3, 9, 16}

c) {3, 7, 8, 9, 13, 16}

A = {x ∈ Z: x is even} C = {3, 5, 9, 12, 15, 16} D = {5, 7, 8, 12, 13, 15} The universal set U is the set of all integers. Select the set corresponding to LaTeX: \overline{\left(A\cup D\right)}\cap\:C ( A ∪ D ) ¯ ∩ C a) {8, 12} b) {5, 12, 15} c) {3, 9} d) {5, 7, 13, 15}

c) {3, 9}

Define the sets A, B, C, and D as follows: A = {-3, 0, 1, 4, 17} B = {-12, -5, 1, 4, 6} C = {x ∈ Z: x is odd} D = {x ∈ Z: x is positive} For the set expression A ∩ B ∩ C, which of the following is the set using roster notation? a) {-5, -3, 0, 1, 4, 17} b) {-12, -5, -3, 0, 1, 4, 6, 17, 1, 4} c) {-12, -5, -3, 0, 1, 4, 6, 17} d) {1}

d) {1}