If A = {x : x ∈ Z, x² = 16} and C = {4}, which statement is correct?
Advertisement
Answer and explanation
Correct answer: C ⊂ A and C ≠ A
Solving x² = 16 over the integers gives x = 4 and x = −4, so A = {−4, 4}. The set C = {4} contains only 4, which belongs to A; therefore C is a subset of A. Since A also contains −4, an element not in C, the sets are not equal. Thus C is a proper subset of A.
Frequently asked questions
What is the correct answer to this question?
C ⊂ A and C ≠ A
Why is this the correct answer?
Solving x² = 16 over the integers gives x = 4 and x = −4, so A = {−4, 4}. The set C = {4} contains only 4, which belongs to A; therefore C is a subset of A. Since A also contains −4, an element not in C, the sets are not equal. Thus C is a proper subset of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement