How many elements are in the set J = {x ∈ ℤ : x² < 4}?
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Answer and explanation
Correct answer: 3
Because x is an integer, we test the integers near zero. The inequality x² < 4 is satisfied by x = -1, 0, and 1, since their squares are 1, 0, and 1. The values x = -2 and x = 2 are excluded because their squares equal 4, not a number less than 4. Thus J = {-1, 0, 1}, which has 3 elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Because x is an integer, we test the integers near zero. The inequality x² < 4 is satisfied by x = -1, 0, and 1, since their squares are 1, 0, and 1. The values x = -2 and x = 2 are excluded because their squares equal 4, not a number less than 4. Thus J = {-1, 0, 1}, which has 3 elements, so option B is correct.
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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