1.3 - Basic Operation on Sets.
1.3.1 - Uinion, Interaction and Diffrence of Sets.
1: What does the union of two sets X and Y represent?
- A) Elements that are only in X
- B) Elements that are only in Y
- C) Elements that are in either X or Y
- D) Elements that are common to both X and Y
Correct Answer: C) Elements that are in either X or Y
2: Which symbol is used to denote the union of two sets?
Correct Answer: A) ∪
3: If X = {1, 3, 5, 7} and Y = {1, 2, 4, 6, 8}, what is X ∪ Y?
- A) {1, 3, 5, 7}
- B) {1, 2, 4, 6, 8}
- C) {1, 2, 3, 4, 5, 6, 7, 8}
- D) {3, 5, 7}
Correct Answer: C) {1, 2, 3, 4, 5, 6, 7, 8}
4: What does the intersection of two sets X and Y represent?
- A) Elements that are only in X
- B) Elements that are only in Y
- C) Elements that are in both X and Y
- D) Elements that are in neither X nor Y
Correct Answer: C) Elements that are in both X and Y
5: Which symbol is used to denote the intersection of two sets?
Correct Answer: B) ∩
6: If X = {1, 3, 5, 7} and Y = {1, 2, 3, 4, 6, 8}, what is X ∩ Y?
- A) {1, 3, 5, 7}
- B) {1, 3}
- C) {2, 4, 6, 8}
- D) {5, 7}
Correct Answer: B) {1, 3}
7: What does the difference X − Y represent in set theory?
- A) Elements that are in both X and Y
- B) Elements that are in X but not in Y
- C) Elements that are in Y but not in X
- D) Elements that are neither in X nor in Y
Correct Answer: B) Elements that are in X but not in Y
8: If X = {1, 2, 3, 4, 5, 6} and Y = {1, 3, 5}, what is X − Y?
- A) {1, 2, 3, 4, 5, 6}
- B) {2, 4, 6}
- C) {1, 3, 5}
- D) {7, 8}
Correct Answer: B) {2, 4, 6}
9: If Y = {a, b, c, d, e, f} and X = {a, e}, what is Y − X?
- A) {a, e}
- B) {b, c, d, f}
- C) {a, b, c, d, e, f}
- D) {b, d}
Correct Answer: B) {b, c, d, f}
10: Which of the following Venn diagram regions represents the set difference X − Y?
- A) The area outside the rectangle representing the universal set
- B) The common area of two circles representing X and Y
- C) The area inside circle X but outside circle Y
- D) The entire area of circle Y
Correct Answer: C) The area inside circle X but outside circle Y
1.3.2 - Cmplement of Set.
11: If U = {a, b, c, d, e, f} and X = {b, d, f}, what is the complement of X relative to U?
- A) {b, d, f}
- B) {a, c, e}
- C) {a, b, c, d, e, f}
- D) {b, c, d, f}
Correct Answer: B) {a, c, e}
12: Which symbol is commonly used to denote the complement of a set X?
- A) X ∪ U
- B) X ∩ U
- C) X'
- D) X
Correct Answer: C) X'
13: In the Venn diagram, which area represents the complement of set X relative to universal set U?
- A) The area inside X
- B) The area outside X but within U
- C) The area overlapping between X and U
- D) The total area of U
Correct Answer: B) The area outside X but within U
14: If U = {1, 2, 3, 4, 5, 6, 7} and X = {1, 3, 5}, what is X'?
- A) {2, 4, 6, 7}
- B) {1, 3, 5}
- C) {2, 4, 6, 7, 1, 3, 5}
- D) {1, 3, 5, 7}
Correct Answer: A) {2, 4, 6, 7}
15: Given U = {x, y, z} and X = {x}, what is X'?
- A) {x}
- B) {y, z}
- C) {x, y, z}
- D) {y}
Correct Answer: B) {y, z}
16: What does the complement of a set X relative to U represent?
- A) All elements in X
- B) Elements in X and U
- C) Elements not in X but in U
- D) All elements in U
Correct Answer: C) Elements not in X but in U
17: If U = {1, 2, 3, 4, 5} and X = {2, 4}, what is the complement of X in U?
- A) {1, 2, 3, 4, 5}
- B) {2, 4}
- C) {1, 3, 5}
- D) {1, 2, 3, 4}
Correct Answer: C) {1, 3, 5}
18: Which of the following statements is true about the complement of a set X?
- A) The complement of X includes all elements of X
- B) The complement of X includes only the elements not in X
- C) The complement of X is the universal set U
- D) The complement of X is the intersection of X and U
Correct Answer: B) The complement of X includes only the elements not in X
19: If X = {a, b} and U = {a, b, c, d}, what is the complement of X in U?
- A) {a, b, c, d}
- B) {a, b}
- C) {c, d}
- D) {b, c}
Correct Answer: C) {c, d}
1.3.3 - Disjoint Sets and Cartesian Product of Two Sets.
20: What defines two sets X and Y as disjoint sets?
- A) X ∩ Y = X
- B) X ∩ Y = Y
- C) X ∩ Y = ∅
- D) X ∪ Y = ∅
Correct Answer: C) X ∩ Y = ∅
21: If X = {2, 4, 6} and Y = {1, 3, 5}, what is X ∩ Y?
- A) {2, 4, 6}
- B) {1, 3, 5}
- C) {2, 3, 5}
- D) ∅
Correct Answer: D) ∅
22: What is the Cartesian product of the sets A = {1, 2, 3} and B = {x, y}?
- A) {(1, x), (1, y), (2, x), (2, y), (3, x), (3, y)}
- B) {(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}
- C) {(1, x), (2, x), (3, x), (1, y), (2, y), (3, y)}
- D) {(x, 1), (y, 1), (x, 2), (y, 2), (x, 3), (y, 3)}
Correct Answer: A) {(1, x), (1, y), (2, x), (2, y), (3, x), (3, y)}
23: What is the Cartesian product B × A if A = {1, 2, 3} and B = {x, y}?
- A) {(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}
- B) {(1, x), (2, x), (3, x), (1, y), (2, y), (3, y)}
- C) {(x, 1), (y, 1), (x, 2), (y, 2), (x, 3), (y, 3)}
- D) {(1, x), (1, y), (2, x), (2, y), (3, x), (3, y)}
Correct Answer: A) {(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}
24: Which of the following pairs of sets are disjoint?
- A) X = {2, 4, 6}, Y = {4, 6, 8}
- B) X = {a, b, c}, Y = {c, d, e}
- C) X = {1, 3, 5}, Y = {2, 4, 6}
- D) X = {x, y, z}, Y = {x, y, z}
Correct Answer: C) X = {1, 3, 5}, Y = {2, 4, 6}
25: If A = {1, 2} and B = {p, q, r}, which of the following is not a member of A × B?
- A) (1, p)
- B) (2, r)
- C) (3, p)
- D) (2, q)
Correct Answer: C) (3, p)
26: What is the Cartesian product A × B if A = {a, b} and B = {1, 2, 3}?
- A) {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
- B) {(1, a), (2, a), (3, a), (1, b), (2, b), (3, b)}
- C) {(a, 1), (a, 2), (b, 3)}
- D) {(1, a), (2, b), (3, a), (3, b)}
Correct Answer: A) {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
27: Which of the following correctly represents B × A if A = {1, 2} and B = {x, y}?
- A) {(x, 1), (y, 1), (x, 2), (y, 2)}
- B) {(1, x), (1, y), (2, x), (2, y)}
- C) {(x, 1), (x, 2), (y, 1), (y, 2)}
- D) {(1, x), (2, x), (1, y), (2, y)}
Correct Answer: A) {(x, 1), (y, 1), (x, 2), (y, 2)}