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Question

If R A × B and S B × C be two relations, then (SoR)1 is equal to

A
S1oR1
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B
RoS
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C
R1oS1
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D
None of these
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Solution

The correct option is C R1oS1
SoR is relation from A to C.
(SoR)1 is a relation from C to A.
R1 is a relation from B to A.
S1 is a relation from C to B.
R1 0S1 is a relation from C to A.
Let (C,a) ϵ (SoR)1. (a,c) ϵ SoR
b ϵ B : (a,b) ϵ R and (b,c) ϵ s
(b,a) ϵ R1 and (c,b) ϵ S1
(c, a) ϵ R1 oS1
(SoR)1 R1 oS1
Conversely, Let (c, a) ϵ R1 oS1
b ϵ B : (c, b) ϵ S1 and (b,a) ϵ R1
(b,c) ϵ S and (a,b) ϵ R
Rightarrow (a,c) ϵ S and (a,b) ϵ R
(a,c) ϵ SoR (c,a) ϵ (SoR)1
R1oS1(SoR)1
Combining, we get (SoR)1=R1oS1

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