(IGP) IAS Pre Paper - 2: GS - Basic Numeracy - Set Theory, Venn Diagrams, Functions & Relations (MCQ -23)

1. The set in set builder form of vowels of English alphabet is
(a) {a, e, i, o, u}
(b) A = {x | x is a vowel in English alphabet)
(c) F
(d) {a, b, c, d, e, f, g}

2. If A = {5} which of the following statement is correct?
(a) A = 5
(b) 5 Ì A
(c) {5} Î A
(d) 5 Î A

3. If A = {a, (b, c), d)}, which of the following is a subset of A.
(a) {a, b}
(b) {b, c}
(c) {c, d}
(d) {a, d}

4. If A Ç B = f nd A and B are two sets, then
(a) AÌ B
(b) B Ì A
(c) A ≠ B
(d) A and B are disjoint

5. If n(A Ç B) = 13, n(A) = 20, n(B) = 44, then n(A È B) = ?
(a) 27
(b) 13
(c) 75
(d) 51

6. n (A) = 6, n(B) = 8, n (A È B) = 12, then n (A Ç B) is
(a) 6
(b) 2
(c) 8
(d) 12
Directions: If A = {1, 2, 3}, B = { 2, 3, 4}, C = {4, 5, 6, 7}

7. B Ç C = ?
(a) {2}
(b) {4}
(c) {2, 4}
(d) {5, 6}

8. A È B = ?
(a) {l, 4}
(b) {2, 3}
(c) {1, 2, 3, 4}
(d) {1, 2}

9. A Ç B = ?
(a) {1, 2, 3, 4}
(b) {2, 3}
(c) {1, 4}
(d) {4, 5}

10. (A È B) È C
(a) {1, 2, 3, 4}
(b) {2, 3, 4, 5, 6, 7}
(c) {1, 2, 3, 4, 5, 6, 7}
(d) {2, 3, 4, 5}

11. (A Ç B) Ç C
(a) {2, 3}
(b) {4}
(c) {1, 2, 3, 4, 5, 6, 7}
(d) Null set

12. Which one of the following statement is correct ?
(a) A Ç B = F = A = F or B = F
(b) A– B = F A Ì B
(c) A Ç B = FA Ì B
(d) A Ç B = A D B

13. The number of all possible subsets of the set {1, {3, 4}} is
(a) 2
(b) 4
(c) 6
(d) 8

14. If A = {1, 2}, then the power set of A is
(a) {1, 2}
(b) {1, 4}
(c) {F,{1},{2}}
(d) {0,11},{21,11,21}

15. The set which is comparable with the set {1, 2, 3, 4} out of the following is
(a) {a, b, c, t}
(b) {2, 3, 4, 5}
(c) {1, 2, 4, 5)
(d) {2, 3, 4}

16. The total number of elements in the power set of A containing n elements is
(a) 2ⁿ
(b) n²
(c) 2ⁿ –1
(d) 2²ⁿ

17. The set {x} (x – 3)(x – 4) > 0} is equal to
(a) {x|3 < x < 4)
(b) {x : x < 4} È {x : x < 3}
(c) {x | x > 4} È {x | x < 3}
(d) None of these

18. Which one of the following is the correct statement?
(a) {x | x + 1 = 1} = 0
(b) {x | x + 1 = 1 is not a set)
(c) {x | x + 1 = 1} = 0
(d) {x | x + 1 = 1} = {0}

19. Which of the following is a true statement ?
(a) {1, 2} Ì ({1}, 2, 3)
(b) {1, 2, a, b) is not a set
(c) {x Î R |3 < x < 4) is finite
(d) {x Î R : | x | = –1) = 0

20. Which one of the following is an infinite set ?
(a) {x |x Î N,x < 40)
(b) {x |x Î  |, x < 40)
(c) {x |x Î |, x is a factor of 400)
(d) {x |x is a whole number, x < 2000}

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