GATE | GATE-IT-2004 | Question 4

Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R₂ be another relation from B to C = {1, 2, 3, 4} as defined below:

An element x in A is related to an element y in B (under R₁) if x + y is divisible by 3.
An element x in B is related to an element y in C (under R₂) if x + y is even but not divisible by 3.

Which is the composite relation R₁R₂ from A to C?

(A)

R1R2 = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)}

(B)

R1R2 = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)}

(C)

R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}

(D)

R1R2 = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}

Answer

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