If {a, 4} = {2, b} and a ≠ 4, which ordered pair (a, b) is correct?
Answer and explanation
Correct answer: (2, 4)
Equal sets must contain exactly the same elements, although the order of listing does not matter. The left-hand set already contains 4. Since a ≠ 4, the other element a must be 2 in order for the set to match {2, b}. Once a = 2, the right-hand set must contain 4 as its second element, so b = 4. Therefore the ordered pair is (2, 4). Option B violates the given condition a ≠ 4, while C and D do not produce the same two-element set.
Frequently asked questions
What is the correct answer to this question?
(2, 4)
Why is this the correct answer?
Equal sets must contain exactly the same elements, although the order of listing does not matter. The left-hand set already contains 4. Since a ≠ 4, the other element a must be 2 in order for the set to match {2, b}. Once a = 2, the right-hand set must contain 4 as its second element, so b = 4. Therefore the ordered pair is (2, 4). Option B violates the given condition a ≠ 4, while C and D do not produce the same two-element set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
