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Let A and B be two sets with n(A) = 2 and n(B) = 3. If the ordered pairs (1, p), (2, q), (1, r) all belong to A x B, where p, q, r are distinct, determine the sets A and B.

1. A = {1, 2}, B = {p, q, r}
2. A = {1, 2, 3}, B = {p, q}
3. A = {p, q}, B = {1, 2, 3}
4. A = {1, p}, B = {2, q, r}

Correct answer: A = {1, 2}, B = {p, q, r}

Solution

From the pairs, the first coordinates are 1 and 2, giving A = {1, 2} with n(A) = 2. The second coordinates are p, q, r (distinct), giving B = {p, q, r} with n(B) = 3.

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