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Sets

Multiple Choice Questions

11.

If S = {x : x² + 1 = 0, r is real}, then S is

{ - 1}
{0}
{1}
an empty set

12.

If E is the universal set and A = B $\cup$ C, then the set E - (E - (E - (E - (E - A)))) is same as the set :

$B' \cup C'$
$B \cup C$
$B' \cap C'$
$B \cap C$

13.

If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then $A \cap (B \cap C)$ is equal to :

A
B
C
{x : x is a multiple of 100}

14.
Let S be a set of all distinct numbers of the form "q' where p. q $\in$ { 1, 2, 3, 4, 5, 6}. What is the cardinality of the set S ?

21

23

32

36

$As \frac{1}{2}, \frac{2}{4}, \frac{3}{6} are same and \frac{1}{1}, \frac{2}{2}, \frac{3}{3}, . . . are same . We will find only co - prime numbers So, when p = 1, q = \{1, 2, 3, 4, 5, 6\} So total elements in S in this case = 6$

When p = 2, q = {1, 3, 5}

So, total elements in S in this case = 3

When p = 3, q = {1, 2, 4, 5}

So, total elements in S in this case = 4

When p = 4, q = {1, 3, 5}

So, total elements in S in this case = 3

When p = 5, q = {1, 2, ,3, 4, 5, 6}

So, total elements in S in this case = 5

When p = 6, q = {1, 5}

So, total elements in S in this case = 2

So, cardinality of set

S = 6 + 3 + 4 + 3 + 5 + 2 = 23

15.

What is the domain of the function f (x) = $\frac{1}{\sqrt{|x| - x}} ?$

$(- \infty, 0)$
$(0, \infty)$
$0 < x < 1$
$x > 1$

16.

Let S = {2, 4, 6, 8, ..........20}. What is the maximum number of subsets does S have ?

10
20
512
1024

17.

If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A U B) can have ?

18.

If A, B and C are subsets of a given set, then which one of the following relations is not correct ?

A U (A ∩ B) = A U B
A ∩ (A U B) = A
(A ∩ B) U C = (A U C) ∩ (B U C)
(A U B) ∩ C = (A ∩ C) U (B ∩ C)

19.

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in z be denoted by n(Z) which is equal to 90

If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X ?

p + b + 60
p + b + 40
p + a + 60
p + a + 40

20.