COS1501 Assignment 1 QUIZ (100% COMPLETE ANSWERS) 2024 (732357) - DUE 10 May 2024

COS1501 Assignment 1 QUIZ (COMPLETE ANSWERS) 2024 (732357) - DUE 10 May 2024 ;100% TRUSTED workings, explanations and soluti ons. for assistance Whats-App.......0.6.7..1.7.1..1.7.3.9........... Which one of the following alternatives is FALSE regarding the number sets Z, Z , Z , Q and R? a. Z ⊆ Z b. Z ⊆ Z c. R ⊆ Q d. Z ⊆ R + ≥ ≥ + ≥ + The set of all non-negative integers x less than 16 such that x is an even integer can be described as the set: (Note: The required set must include as elements all non-negative integers x such that all the requirements for the set aremet.) a. {x| x ∈ Z , x < 16, x = 2k for some k ∈ Z} b. {x| x ∈ Z , x < 16, x = 2k for some k ∈ Z } c. {0, 2, 4, 16, 36, 64, 100, 144, 196} d. {0, 2, 4} 2 ≥ 2 ≥ 2 + Question 3 Complete Marked out of 2.00 Question 4 Complete Marked out of 2.00 Question 5 Complete Marked out of 2.00 {x| x ∈ Z, 0 ≤ x < 8} ⋂ {x| x ∈ R, 4 ≤ x < 16} is the set: a. {x| x ∈ R, 4 ≤ x < 8} b. {x| x ∈ Z, 0 ≤ x ≤ 8} c. {x| x ∈ Z, 0 ≤ x ≤16} d. {4, 5, 6, 7} Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} A U B is the set: a. {1, 2, {1}, {1, 2}} b. {1, 2, {1, 2}} c. {{1}, {1, 2}} d. {{1}} Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} A ⋂ C is the set: a. {2, {1, 2}} b. {1, 2, {1}} c. {2, {1}, {2}} d. {2, {1}} Question 6 Complete Marked out of 2.00 Question 7 Complete Marked out of 2.00 Question 8 Complete Marked out of 2.00 Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} A – B is the set: a. {1, 2} b. {1, {1, 2}} c. { } d. {{1, 2}} Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} B + C is the set: a. {{1, 2}} b. {{1}, {2}} c. {2, {2}, {1, 2}} d. {2, {1}, {2}, {1, 2}} Let A = {{⊘}, 1, {1}}. Which one of the following alternatives regarding A is FALSE? a. {{1}} ⊂ A b. {⊘} ⊂ A c. |Ƥ (A)| = 8 d. {⊘} ∈ A Question 9 Complete Marked out of 2.00 Question 10 Complete Marked out of 2.00 Question 11 Complete Marked out of 2.00 U = {a, b, c, d, e} A = {d, e} B = {a, b, c}. Which one of the following statements regarding the given sets is FALSE? a. A’ – U = {d, e} b. (A ⋂ B) + U = {a, b, c, d, e} c. (U ⋂ B’) = B’ d. (U – A) + B = U – (A + B) U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2} } . Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).) a. x ∈ {1}. b. x ∈ ⊘. c. x ∈ {1, 2}. d. x ∈ B and x ∈ C. U = {a, b, c, d, e} A = {d, e} B = {a, b, c}. Which one of the following statements regarding the sets U, A and B is TRUE? a. | Ƥ (U) | = | Ƥ (A) | + | Ƥ (B)| b. ⊘ ⊂ Ƥ (A) and ⊘ ⊂ Ƥ (B) c. U – A = A – U d. A + B = U Question 12 Complete Marked out of 2.00 Question 13 Complete Marked out of 2.00 Question 14 Complete Marked out of 2.00 Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} Ƥ (A) is the set: a. {⊘, {1}, {2}, {1, 2}, {1, 2, {1}}} b. {⊘, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, {1, 2, {1}}} c. {⊘, {1}, {2}, {{1, 2}}, {1, {1}}, {2, {1}}, {1, 2, {1, 2}}} d. {⊘, {1}, {2}, {{1}}, {1, {1}}, {2, {1}}, {1, 2, {1}}} U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2} } . Which one of the following sets represents both Ƥ (A) ⋂ Ƥ (B) and Ƥ (A ⋂ B)? a. {{1}} b. {⊘, {{1}}} c. {⊘, {1}} d. Not one of the above alternatives since Ƥ (A) ⋂ Ƥ (B) ≠ Ƥ (A ⋂ B) U = { 1, 2, {1}, {2}, {1, 2} } A = { 1, 2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2} } . Which one of the following is a subset of Ƥ (A)? (Remember, s ubsets of some set G can be formed by keeping the outside brackets of G and then throwingaway none , one or more elements of G. Refer to study guide, p 40.) a. {1} b. {1, 2, {1, 2}} c. {{{1}}} d. {{{2}}} Question 15 Complete Marked out of 2.00 Which one of the following defi nitions is a correct defi nition for symmetric set difference? a. The complement of B relative to A is denoted by A – B, and is the set of all those elements of A which do not belongto B. More briefl y A – B = {x | x ∈ A and x ∉ B}. This is also referred to as the difference between sets A and B. b. The symmetric difference between two sets A and B, written as A - B, is defi ned as the set of all elements that belongto B, but not to A. More briefl y, A - B = { x | x ∉ A and x ∈ B} c. The symmetric difference between two sets A and B, written as A + B, is defi ned as the set of all elements thatbelong to A or to B. More briefl y, A + B = { x | x ∈ A or x ∈ B} d. The symmetric difference between two sets A and B, written as A + B, is defi ned as the set of all elements thatbelong to A or to B, but not to both A and B. More briefl y, A + B = { x | x ∈ A or x ∈ B, but not both}