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Question

# Which of the following are relations from the set A={1,2,3,4} to set B={a,b,c}?

A

{(1,a),(1,b),(1,c)}

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B

{(2,a),(2,b),(2,c)}

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C

{(3,a),(3,b),(3,c)}

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D

{(4,a),(4,b),(4,c)}

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Solution

## The correct options are A {(1,a),(1,b),(1,c)} B {(2,a),(2,b),(2,c)} C {(3,a),(3,b),(3,c)} D {(4,a),(4,b),(4,c)} A relation R from a non-empty set A to a non-empty set B is a subset of A×B. Given that A={1,2,3,4} and B={a,b,c}. ⇒A×B={(1,a),(1,b),(1,c),(2,a),(2,b),(2,c),(3,a),(3,b),(3,c),(4,a),(4,b),(4,c)} Note that {(1,a),(1,b),(1,c)}⊆A×B, {(2,a),(2,b),(2,c)}⊆A×B, {(3,a),(3,b),(3,c)}⊆A×B and {(4,a),(4,b),(4,c)}⊆A×B. Thus, they are all relations from A to B.

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