COS1501-Ass 1 2023 with 100% correct questions and answers

Which one of the following alternatives is FALSE regarding the number sets Z, Z+ , Z≥ , Q and R? Z≥ Z Z+ Z≥ R Q Z+ R R Q Which one of the following definitions is a correct definition for symmetric set difference? 1. 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 belong to B. More briefly A - B = {x | x A and x B}. This is also referred to as the difference between sets A and B. 2. The symmetric difference between two sets A and B, written as A - B, is defined as the set of all elements that belong to B, but not to A. More briefly, A - B = { x | x ∉ A and x B} 3. The symmetric difference between two sets A and B, written as A + B, is defined as the set of all elements that belong to A or to B. More briefly, A + B = { x | x A or x B} 4. The symmetric difference between two sets A and B, written as A + B, is defined as the set of all elements that belong to A or to B, but not to both A and B. More briefly, A + B = { x | x A or x B, but not both} 4. The symmetric difference between two sets A and B, written as A + B, is defined as the set of all elements that belong to A or to B, but not to both A and B. More briefly, A + B = { x | x A or x B, but not both} The set of all non-negative integers x less than 16 such that x2 is an even integer can be described as the set: 1. {x x Z≥ , x 16, x 2 = 2k for some k Z} 2. {x x Z≥ , x 16, x 2 = 2k for some k Z+ } 3. {0, 2, 4, 16, 36, 64, 100, 144, 196} 4. {0, 2, 4} (Note: The required set must include as elements all non-negative integers x such that all the requirements for the set are met.) 2. {x x Z≥ , x 16, x 2 = 2k for some k Z+ } {x x Z, 0 x 8} {x x R, 4 x 16} is the set: 1. {x x R, 4 x 8} 2. {x x Z, 0 x 8} 3. {x x Z, 0 x 16} 4. {4, 5, 6, 7} 1. {x x R, 4 x 8} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) A B is the set: 1. {1, 2, {1}, {1, 2}} 2. {1, 2, {1, 2}} 3. {{1}, {1, 2}} 4. {{1}} 1. {1, 2, {1}, {1, 2}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) A C is the set: 1. {2, {1, 2}} 2. {1, 2, {1}} 3. {2, {1}, {2}} 4. {2, {1}} 4. {2, {1}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) A - B is the set: 1. {1, 2} 2. {1, {1, 2}} 3. { } 4. {{1, 2}} 1. {1, 2} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) B + C is the set: 1. {{1, 2}} 2. {{1}, {2}} 3. {2, {2}, {1, 2}} 4. {2, {1}, {2}, {1, 2}} 4. {2, {1}, {2}, {1, 2}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) Ƥ (A) is the set: 1. {0/, {1}, {2}, {1, 2}, {1, 2, {1}}} 2. {0/ , {1}, {2}, {{1}}, {1, 2} {1, {1}}, {2, {1}}, {1, 2, {1}}} 3. {0/, {1}, {2}, {{1, 2}}, {1, {1}}, {2, {1}}, {1, 2, {1, 2}}} 4. {0/ , {1}, {2}, {{1}}, {1, {1}}, {2, {1}}, {1, 2, {1}}} 1. {0/, {1}, {2}, {1, 2}, {1, 2, {1}}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) Which one of the following is a subset of Ƥ (A)? 1. {1} 2. {1, 2, {1, 2}} 3. {{{1}}} 4. {{{2}}} 2. {1, 2, {1, 2}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) Which one of the following sets represents both Ƥ (A) Ƥ (B) and Ƥ (A B)? 1. {{1}} 2. {0/, {{1}}} 3. {0/, {1}} 4. Not one of the above alternatives since Ƥ (A) Ƥ (B) Ƥ (A B) 2. {0/, {{1}}} Consider the following sets, where U represents a universal set: U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}. (Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3 elements, B has 2 elements and C has 3 elements. List the elements of A, B and C before answering the questions.) Which one of the following statements is valid if x B C? (Hint: Determine U - (B C).) 1. x {1}. 2. x 0/. 3. x {1, 2}. 4. x B and x C 1. x {1}. Consider the following sets, where U represents a universal set: 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? 1. | Ƥ (U) | = | Ƥ (A) | + | Ƥ (B)| 2. 0/ Ƥ (A) and 0/ Ƥ (B) 3. U - A = A - U 4. A + B = U 4. x B and x C Consider the following sets, where U represents a universal set: 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? 1. A - U = {d, e} 2. (A B) + U = {a, b, c, d, e} 3. (U B) = B 4. (U - A) + B = U - (A + B) 4. (U - A) + B = U - (A + B)