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. R1 = {(p, 1), (q, 2), (r, 1), (s, 2)}

ii. R2 = {(p, 1), (q, 1), (r, 1), (s, 1)}

iii. R3 = {(p, 1), (q, 2), (p, 2), (s, 3)}

iv. R4 = {(p, 2), (q, 3), (r, 2), (s, 2)}

Answer :

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


i. R1 = {(p, 1), (q, 2), (r, 1), (s, 2)}


Every element of set A has an ordered pair in the relation R1 and no two ordered pairs have the same first component but different second components.


Hence, the given relation R1 is a function.


ii. R2 = {(p, 1), (q, 1), (r, 1), (s, 1)}


Every element of set A has an ordered pair in the relation R2, and no two ordered pairs have the same first component but different second components.


Hence, the given relation R2 is a function.


iii. R3 = {(p, 1), (q, 2), (p, 2), (s, 3)}


Every element of set A has an ordered pair in the relation R3. However, two ordered pairs (p, 1) and (p, 2) have the same first component but different second components.


Hence, the given relation R3 is not a function.


iv. R4 = {(p, 2), (q, 3), (r, 2), (s, 2)}


Every element of set A has an ordered pair in the relation R4, and no two ordered pairs have the same first component but different second components.


Hence, the given relation R4 is a function.


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