Refer to the table below Does the set A 1 2 3 4 have an ide

Refer to the table below. Does the set A = {1, 2, 3, 4} have an identity under the operation S? Yes No If so, what is this identity? (If an answer does not exist, enter DNE.)

Solution

A set A is said to have an identity element with respect to the operation S , if for any element x A , there exists an element e A such that x S e = e S x = x .

Fro the given table we can observe that

4 S 1 = 1

4 S 2 = 2

4 S 3 = 3

4 S 4 = 4

hence the identity element in the A = { 1 , 2, 3 , 4 } is 4