On the integers, define aRb when a+b is even. Is R transitive?
Answer and explanation
Correct answer: Yes, because parity is preserved
The condition aRb means that a and b have the same parity: both are even or both are odd. If aRb and bRc, then a and b have the same parity, and b and c also have the same parity. Consequently, a and c have the same parity, so a+c is even and aRc. The argument works for all integers, including negative values, so A is correct.
Frequently asked questions
What is the correct answer to this question?
Yes, because parity is preserved
Why is this the correct answer?
The condition aRb means that a and b have the same parity: both are even or both are odd. If aRb and bRc, then a and b have the same parity, and b and c also have the same parity. Consequently, a and c have the same parity, so a+c is even and aRc. The argument works for all integers, including negative values, so A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
