Q. 145.0( 2 Votes )

# Let A = {p, q, r, s} and B = {1, 2, 3}. Which of the following relations from A to B is not a function?

i. R_{1} = {(p, 1), (q, 2), (r, 1), (s, 2)}

ii. R_{2} = {(p, 1), (q, 1), (r, 1), (s, 1)}

iii. R_{3} = {(p, 1), (q, 2), (p, 2), (s, 3)}

iv. R_{4} = {(p, 2), (q, 3), (r, 2), (s, 2)}

Answer :

Given A = {p, q, r, s} and B = {1, 2, 3}

i. R_{1} = {(p, 1), (q, 2), (r, 1), (s, 2)}

Every element of set A has an ordered pair in the relation R_{1} and no two ordered pairs have the same first component but different second components.

Hence, the given relation R_{1} is a function.

ii. R_{2} = {(p, 1), (q, 1), (r, 1), (s, 1)}

Every element of set A has an ordered pair in the relation R_{2,} and no two ordered pairs have the same first component but different second components.

Hence, the given relation R_{2} is a function.

iii. R_{3} = {(p, 1), (q, 2), (p, 2), (s, 3)}

Every element of set A has an ordered pair in the relation R_{3}. However, two ordered pairs (p, 1) and (p, 2) have the same first component but different second components.

Hence, the given relation R_{3} is not a function.

iv. R_{4} = {(p, 2), (q, 3), (r, 2), (s, 2)}

Every element of set A has an ordered pair in the relation R_{4,} and no two ordered pairs have the same first component but different second components.

Hence, the given relation R_{4} is a function.

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