If A = {x ∈ Z : −5 ≤ x ≤ 5 and x ≡ 1 (mod 3)} and B = {−5, −2, 1, 4}, which conclusion is correct?
Answer and explanation
Correct answer: A = B, because both have the same four elements
The integers from −5 to 5 that are congruent to 1 modulo 3 are −5, −2, 1, and 4. For example, each differs from 1 by a multiple of 3: −6, −3, 0, and 3 respectively. Hence A = {−5, −2, 1, 4} = B. Set equality depends on having exactly the same elements, not on their order or on whether the elements are positive or negative. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B, because both have the same four elements
Why is this the correct answer?
The integers from −5 to 5 that are congruent to 1 modulo 3 are −5, −2, 1, and 4. For example, each differs from 1 by a multiple of 3: −6, −3, 0, and 3 respectively. Hence A = {−5, −2, 1, 4} = B. Set equality depends on having exactly the same elements, not on their order or on whether the elements are positive or negative. Therefore 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.
