- 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.
Answer:(C)
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)
Thus, R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}
Thus, option (C) is correct.
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