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If A = [1, 2, 3], B = [4, 5, 6],

Question:

If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]

(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]

(iii) [(4, 2), (4, 3), (5, 1)]

(iv) A × B.

Solution:

Given:
A = {1, 2, 3} and B = {4, 5, 6}
Thus, we have:

A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

(i) {(1, 6), (3, 4), (5, 2)}

Since it is not a subset of A × B, it is not a relation from A to B.

(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}

Since it is a subset of A × B, it is a relation from A to B.

(iii) {(4, 2), (4, 3), (5, 1)}

Since it is not a subset of A × B, it is not a relation from A to B.

(iv) A × B

Since it is a subset (equal to) of A × B, it is a relation from A to B.

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