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)}

Question

Philoid · Accepted 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 R_2, 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 R_4, and no two ordered pairs have the same first component but different second components.

Hence, the given relation R₄ is a function.

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)}

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)}