Related Articles

GATE | GATE-IT-2004 | Question 4

• Last Updated : 14 Feb, 2018

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:

1. An element x in A is related to an element y in B (under R1) if x + y is divisible by 3.
2. 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)}

Explanation:
R1 is a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} .
Under R1, an element x in A is related to an element y in B if x + y is divisible by 3.

Thus, R1 = {(1, 2), (1, 8), (3, 6), (5, 4), (7, 2), (7, 8)}

R2 is a relation from B = {2, 4, 6, 8} to C = {1, 2, 3, 4}
Under R2, an element y in B is related to an element z in C if y + z is even but not divisible by 3.

Thus, R2 = {(2, 2), (4, 4), (6, 2), (6, 4), (8, 2)}

Then the composition of R1 with R2, denoted R2R1, is the relation from A to C defined by the following property: (x, z) R2R1 If and only if there is a y E B such that (x, y) R1 and (y, z) R2.

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

Thus, option (C) is correct.

Please comment below if you find anything wrong in the above post.

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up