If C={x:x²=16, x∈Z}, how many elements does C have?
Answer and explanation
Correct answer: 2
The governing concept is solving a square equation over the integers and then counting distinct set elements. From x²=16, we obtain x=4 or x=-4 because both values have square 16. Thus C={-4,4}, which contains two distinct elements. The value 16 is the square on the right side, not the cardinality, and 4 is only one solution. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing concept is solving a square equation over the integers and then counting distinct set elements. From x²=16, we obtain x=4 or x=-4 because both values have square 16. Thus C={-4,4}, which contains two distinct elements. The value 16 is the square on the right side, not the cardinality, and 4 is only one solution. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Common Questions. Topic: Squares and Square Roots.
