How many elements are in E = {x ∈ ℤ : x² = 9 or x² = 16}?
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Answer and explanation
Correct answer: 4
For x² = 9, the integer solutions are x = −3 and x = 3. For x² = 16, the integer solutions are x = −4 and x = 4. These four values are different, so E = {−4, −3, 3, 4}. Consequently, the cardinality of E is 4, making option C correct. Both positive and negative square roots must be included.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For x² = 9, the integer solutions are x = −3 and x = 3. For x² = 16, the integer solutions are x = −4 and x = 4. These four values are different, so E = {−4, −3, 3, 4}. Consequently, the cardinality of E is 4, making option C correct. Both positive and negative square roots must be included.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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