Discussion

Question:

Let A and B be two sets such that the Cartesian product A × B consists of four elements. If two elements of A × B are (1,4) and (4,1), then

Explanation:

2 elements of A × B are (1,4) and (4,1).

∴ 1 and 4 are elements of A and 4 and 1 are elements of B.
⇒ Both A and B have at least 2 elements.

Now, A × B has 4 elements and both A and B have at least 2 elements. This is possbile when both A and B have exactly 2 elements each.

⇒ A = {1, 4} and B = {4, 1}

⇒ A × B = {(1, 4), (1, 1), (4, 4), (4, 1)}

Also, B × A = {(4, 1), (4, 4), (1, 1), (1, 4)}

We can see that A × B = B × A.

Hence, option (d).

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