If A = {2, 4, 6} and B = {x : x is a positive even number and x < 8}, which statement is correct?
Answer and explanation
Correct answer: A = B
To expand B, list the positive even integers less than 8. They are 2, 4, and 6; 8 is not allowed because the inequality is strict, and neither 0 nor negative even numbers are positive. Therefore B = {2,4,6}, which has exactly the same elements as A. Hence A = B. Options B and C incorrectly claim a proper-subset relation, while option D is false because A ∩ B = {2,4,6}, not the empty set.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To expand B, list the positive even integers less than 8. They are 2, 4, and 6; 8 is not allowed because the inequality is strict, and neither 0 nor negative even numbers are positive. Therefore B = {2,4,6}, which has exactly the same elements as A. Hence A = B. Options B and C incorrectly claim a proper-subset relation, while option D is false because A ∩ B = {2,4,6}, not the empty 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.
