If U = {x ∈ Z : -5 ≤ x ≤ 15} and A = {x ∈ U : x ≡ 2 (mod 5)}, what is n(A')?
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Answer and explanation
Correct answer: 17
The integers from -5 through 15 inclusive number 15 - (-5) + 1 = 21, so n(U) = 21. The members congruent to 2 modulo 5 in this interval are -3, 2, 7, and 12, giving n(A) = 4. Since A' is the complement within U, n(A') = n(U) - n(A) = 21 - 4 = 17. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The integers from -5 through 15 inclusive number 15 - (-5) + 1 = 21, so n(U) = 21. The members congruent to 2 modulo 5 in this interval are -3, 2, 7, and 12, giving n(A) = 4. Since A' is the complement within U, n(A') = n(U) - n(A) = 21 - 4 = 17. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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