If A = {x : x ∈ ℕ, x² = 49} and B = {7}, which statement is correct?
Answer and explanation
Correct answer: A = B
The governing concept is equality of sets together with the stated domain restriction. Algebraically, x² = 49 gives x = 7 or x = −7. However, x must belong to the natural numbers, so −7 is excluded and A = {7}. Since B is also the singleton set {7}, A and B have exactly the same element. Thus option A is correct; option C ignores the domain restriction.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The governing concept is equality of sets together with the stated domain restriction. Algebraically, x² = 49 gives x = 7 or x = −7. However, x must belong to the natural numbers, so −7 is excluded and A = {7}. Since B is also the singleton set {7}, A and B have exactly the same element. Thus option A is correct; option C ignores the domain restriction.
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.
