### Set Theory Problems with answers:

If two sets *A* and *B* have 99 elements in common, then the number of elements common to each of the sets A x B and B x A are

(a) 2^{99}

(b) 99^{2
}(c) 100

(d) 18

If the set *A *has *p *elements, *B *has *q* elements, then the number of elements in *A *Ã— *B* is

(a) p + q

(b) p + q + 1

(c) pq

(d) p^{2}

A and B are subsets of a universal set having 12 elements. If A has 7 elements, B has 9 elements and Aâˆ©B has 9 elements , then what is the number of elements in AâˆªB ?

(a) 11

(b) 16

(c) 22

(d) 10

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The set of intelligent students in a class is

(a) A null set

(b) A singleton set

(c) A finite set

(d) Not a well defined collection

If A = {1, 2, 3, 4}, then the number of non-empty subsets of A is

(a) 16

(b) 15

(c) 32

(d) 3

Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, and 12 play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is

(a) 43

(b) 76

(c) 49

(d) None of these

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Which of the following is the empty set?

(a) {*x *: *x *is a real number and x^{2} â€“ 1 = 0}

(b) {*x *: *x *Â is a real number and x^{2} + 1 = 0}

(c) {*x *: *x* is a real number and x^{2} â€“ 9 = 0

(d) {*x *: *x* is a real number and x^{2} = x + 2

If a set A has 3 elements and B has 6 elements, then the minimum number of elements in AâˆªB is

(a) 6

(b) 3

(c) 9

(d) None of these

If a set *A *has *n *Â elements, then the total number of subsets of *A *Â is

(a)* n*

(b) n^{2
}(c) 2^{n}

(d) 2n

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If (1, 3), (2, 5) and (3, 3) are three elements of *A *x *B* and the total number of elements in A x B is 6, then the remaining elements of A x B are

(a) (1, 5); (2, 3); (3, 5)

(b) (5, 1); (3, 2); (5, 3)

(c) (1, 5); (2, 3); (5, 3)

(d) None of these

The set of all prime numbers is

(a) A finite set

(b) A singleton set

(c) An infinite set

(d) None of these

A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

(a) 35

(b) 48

(c) 60

(d) 22

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The number of proper subsets of the set {1, 2, 3} is

(a) 8

(b) 7

(c) 6

(d) 5

In a town of 10000 families it was found that 40% of families buy newspaper *A*, 20% buy newspaper *B *and 10% of families buy newspaper *C*, 5% of families buy *A *and *B*, 3% buy *B* and *C *and 4% buy *A *and *C*. If 2% the families buy all the three newspapers, then number of families which buy *A *only is

(a) 3100

(b) 3300

(c) 2900

(d) 1400

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In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is

(a) 80 percent

(b) 40 percent

(c) 60 percent

(d) 70 percent

Let S = {0, 1, 5, 4, 7}. Then the total number of subsets of *S* is

(a) 64

(b) 32

(c) 40

(d) 20

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A set contains 2n + 1 elements. The number of subsets of this set containing more than *n* elements is equal to

(a) 2^{n â€“ 1}

(b) 2^{n
}(c) 2^{n + 1}

(d) 2^{2n}

20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is

(a) 12

(b) 8

(c) 16

(d) None of these

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In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, *x*% lost all the four limbs. The minimum value of *x* is

(a) 10

(b) 12

(c) 15

(d) None of these

If *A *= {1, 2, 4}, *B *= {2, 4, 5}, *C *= {2, 5}, then (*A* â€“ *B*) x (*B* â€“ *C*) is

(a) {(1, 2), (1, 5), (2, 5)}

(b) {(1, 4)}

(c) (1, 4)

(d) None of these

If n(A) = 4, n(B) = 3, n(A x B x C) = 24, then n(C) =

(a) 288

(b) 1

(c) 12

(d) 2

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In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is

(a) 16

(b) 6

(c) 8

(d) 20

### What is Set Theory?

Set theory is a fundamental concept in mathematics. Its definitions include numbers, functions and functionals, as well as geometric and topological concepts. It is often referred to as the Foundations of Mathematics, since any question of mathematical provability can be reduced to its formal derivation.

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