Relations and Functions Test

Result

Relations and Functions Test - 25

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Question 1
1 / -0

What is the number of equivalence relation in the set {2, 3, 4}. Containing (2, 3) & (3, 2) ?

A
Zero

B
One

C
Three

D
Two

Solution

Given,

set A = {2, 3, 4}

R₁ = {(2, 2), (3, 3), (4, 4), (2, 3), (3, 2) = Smallest equivalence Relation R₁ containing (2, 3) & (3, 2)

There,

(3, 4), (4, 3), (2, 4), (4, 2) are not in R₁

If we add (3, 4) ⇒ for symmetricity we must add (4, 3) and for transitivity we must add (2, 4) & (4, 2)

Thus, the total number of equivalence relation containing (2, 3) & (3, 2) is two.
Question 2
1 / -0

If the composition of function is given as f : A → B & g : B → C is the function gof : A → C is given by gof(x) = g(f(x)), ∀ x ∈ A

where

f(x) = -x + 2 & g(x) = 2x

then gof. is ....

A
-2x + 4

B
2x + 4

C
-(2x + 4)

D
2x - 4

Solution

Given,

f(x) = -x + 2 & g(x) = 2x

Then,

For gof

gof(x) = g(f(x))

⇒ gof (x) = g(-x + 2)

⇒ gof(x) = 2(-x + 2)

gof(x) = -2x + 4

∴ gof = (-2x + 4)