If A = {x ∈ Z : x ≡ 2 (mod 5) and −6 ≤ x ≤ 6}, what is A equal to?
Advertisement
Answer and explanation
Correct answer: {−3, 2}
The integers between −6 and 6 that are congruent to 2 modulo 5 can be found from x = 5k + 2. For k = −1, x = −3; for k = 0, x = 2; while k = 1 gives 7, which is outside the interval. Therefore the only eligible elements are −3 and 2, so A = {−3, 2}. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{−3, 2}
Why is this the correct answer?
The integers between −6 and 6 that are congruent to 2 modulo 5 can be found from x = 5k + 2. For k = −1, x = −3; for k = 0, x = 2; while k = 1 gives 7, which is outside the interval. Therefore the only eligible elements are −3 and 2, so A = {−3, 2}. Hence option A 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.
Advertisement