If A = {x ∈ Z | x² = 16} and B = {−4, 4}, which statement is true?
Answer and explanation
Correct answer: A = B
Solving x² = 16 over the integers gives x = 4 or x = −4. Therefore A = {−4, 4}. The set B is also defined as {−4, 4}, so A and B contain exactly the same elements and are equal. Thus option A is true. Option B omits −4, option C incorrectly claims a proper inclusion even though the sets are equal, and option D is false because A has two elements.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Solving x² = 16 over the integers gives x = 4 or x = −4. Therefore A = {−4, 4}. The set B is also defined as {−4, 4}, so A and B contain exactly the same elements and are equal. Thus option A is true. Option B omits −4, option C incorrectly claims a proper inclusion even though the sets are equal, and option D is false because A has two elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
