Question

Let A = set of all positive integers. A relation R is defined by:
$aRb\iff (a-b)isdivisibleby4.$
R is an equivalence relation on A.
The equivalence class of 3 =

• A. {0,4,8,12, ........}
• B. {1,5,9,13, ........}
• C. {2,6,10,14, ........}
• D. {3,7,11,15, ........}

Answer 1

The correct option is D {3,7,11,15, ........}

option (c)

The equivalence class of
x = {y | x - y is divisible by 4}

Equivalence class of 3
= {y |3 - y is divisible by 4}
= {4n + 3| n is a non-negative integer}
= {3, 7, 11, 15, ......}