If R = {x : x ∈ Z, x² = 16}, what are the elements of R?
Answer and explanation
Correct answer: R = {-4, 4}
To find the elements, solve the defining equation x² = 16. Taking square roots gives x = 4 or x = −4, since both 4² = 16 and (−4)² = 16. Both values are integers and therefore satisfy the domain condition x ∈ Z. Thus R = {−4, 4}. Option A omits one valid solution, option C confuses the square with the value of x, and option D wrongly claims that no solution exists.
Frequently asked questions
What is the correct answer to this question?
R = {-4, 4}
Why is this the correct answer?
To find the elements, solve the defining equation x² = 16. Taking square roots gives x = 4 or x = −4, since both 4² = 16 and (−4)² = 16. Both values are integers and therefore satisfy the domain condition x ∈ Z. Thus R = {−4, 4}. Option A omits one valid solution, option C confuses the square with the value of x, and option D wrongly claims that no solution exists.
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.
