Relations and Functions Test

Result

Relations and Functions Test - 10

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Question 1
1 / -0

The range of the function f (x) = cos (x/3) is

A
[-3, 3]

B
[−1/3,1/3]

C
[ - 1, 1]

D
none of these

Solution

Since the cosine function takes values between

- 1 and 1 including - 1 and 1 also.

∴ range of given function = [-1,1]
Question 2
1 / -0

If n (A) = 10, n (B) = 6 and n (C) = 5 for three disjoint sets A, B and C, then n(A ∪ B ∪ C)=

A
11

B
21

C
1

D
9

Solution

Since A, B, C are disjoint

∴ n(A ∪ B ∪ C) = n(A) + n(B) + n(C)

= 10 + 6 + 5 = 21
Question 3
1 / -0

If B is the set of numbers obtained by adding 1 to each of the even numbers, then its set builder notation is

A
B = {x : x is an integer}

B
B = {x ; x is odd and x ∈ Z}

C
B = {x : x is odd and x >1}

D
B = {x : x is even }

Solution

If we add an odd and 1 then we get even number

∴ B = { x : x is odd and x ∈ z}
Question 4
1 / -0

The relation R = {1, 1), (2, 2), (3, 3)} on the set {1, 2, 3) is

A
symmetric only

B
transitive only

C
an equivalence relation

D
reflexive only