If C = {x : x ∈ ℤ, −5 < x < 5, x is odd, and x² > 9}, how many elements does C have?
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Answer and explanation
Correct answer: 0
The integers satisfying −5 < x < 5 are −4, −3, −2, −1, 0, 1, 2, 3, and 4. Among these, the odd integers are −3, −1, 1, and 3. Their squares are 9, 1, 1, and 9 respectively. None has x² > 9; the values −3 and 3 only give x² = 9, which is not greater than 9. Therefore, C is the empty set and has 0 elements.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The integers satisfying −5 < x < 5 are −4, −3, −2, −1, 0, 1, 2, 3, and 4. Among these, the odd integers are −3, −1, 1, and 3. Their squares are 9, 1, 1, and 9 respectively. None has x² > 9; the values −3 and 3 only give x² = 9, which is not greater than 9. Therefore, C is the empty set and has 0 elements.
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.
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