Question

Let R be the relation defined on Z (integers): a R b iff a + b is even. Then the distinct equivalence classes are:

Group of answer choices

[1] = multiples of 3

[2] = multiples of 4

[0] = even integers and [1] = the odd integers

all the integers

None of the above

Answer 1

For a sum to be even, either both the numbers should be even or both or them should be odd, then only the sum of two integers can be an even integer. So answer will be:

[0] = even integers and [1] = the odd integers