If A is the set of integers that leave remainder 1 when divided by 2, which statement about A is correct?
Answer and explanation
Correct answer: A is infinite
An integer that leaves remainder 1 on division by 2 is odd. The set can be written as A = {2k + 1 : k ∈ Z}, which includes ..., -5, -3, -1, 1, 3, 5, ... . Since k can be any integer and there is no largest or smallest member, the set contains infinitely many elements. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
A is infinite
Why is this the correct answer?
An integer that leaves remainder 1 on division by 2 is odd. The set can be written as A = {2k + 1 : k ∈ Z}, which includes ..., -5, -3, -1, 1, 3, 5, ... . Since k can be any integer and there is no largest or smallest member, the set contains infinitely many elements. 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.
