What is the nature of A = {x ∈ Z : x ≡ 2 (mod 5)}?
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Answer and explanation
Correct answer: Infinite set
The congruence x ≡ 2 (mod 5) means that x has the form x = 5k + 2, where k is any integer. Taking k = 0, 1, 2 gives 2, 7, 12, while k = −1, −2 gives −3, −8. Since there are infinitely many possible integer values of k, there are infinitely many elements in A. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
The congruence x ≡ 2 (mod 5) means that x has the form x = 5k + 2, where k is any integer. Taking k = 0, 1, 2 gives 2, 7, 12, while k = −1, −2 gives −3, −8. Since there are infinitely many possible integer values of k, there are infinitely many elements in A. Thus option C is correct.
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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