If A = {x ∈ ℤ : x is odd and x² = 16}, then what is A?
Answer and explanation
Correct answer: ∅ — रिक्त समुच्चय
From x² = 16, we obtain x = 4 or x = −4. However, the definition of A also requires x to be an odd integer. Both 4 and −4 are even, so neither value satisfies all the stated conditions simultaneously. Therefore, there is no element in A, and A is the empty set, written as ∅. The answer is option A.
Frequently asked questions
What is the correct answer to this question?
∅ — रिक्त समुच्चय
Why is this the correct answer?
From x² = 16, we obtain x = 4 or x = −4. However, the definition of A also requires x to be an odd integer. Both 4 and −4 are even, so neither value satisfies all the stated conditions simultaneously. Therefore, there is no element in A, and A is the empty set, written as ∅. The answer is option A.
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.
