If A = {-1, 0, 1, 2} and B = {0, 1, 2}, how many ordered pairs (x, y) in A × B satisfy x + y = 1?
Advertisement
Answer and explanation
Correct answer: 3
Rewrite the condition as y = 1 - x and test the elements of A. For x = -1, y = 2, giving (-1,2); for x = 0, y = 1, giving (0,1); for x = 1, y = 0, giving (1,0); and for x = 2, y = -1, which is not in B. Thus exactly three ordered pairs belong to A × B and satisfy the equation. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Rewrite the condition as y = 1 - x and test the elements of A. For x = -1, y = 2, giving (-1,2); for x = 0, y = 1, giving (0,1); for x = 1, y = 0, giving (1,0); and for x = 2, y = -1, which is not in B. Thus exactly three ordered pairs belong to A × B and satisfy the equation. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement