Question

Construct Cayley’s table for the following

(1) Z₅ under addition modulo 5.

(2) Z₆ under addition modulo 6.

(3) Z₃ under addition modulo 3.

(4) Z₄ under addition modulo 4.

(5) Q = {0, 2, 4, 6, 8} under ⊕ mod 10.

(6) S = {1, 5, 7, 11} under ⊗ mod 12.

Answer 1

(1) We need to construct Cayley’s table for under addition modulo 5.

Here,

Hence, Cayley’s table for under addition modulo 5 can be given as follows:

(2) We need to construct Cayley’s table for under addition modulo 6.

Here,

Hence, Cayley’s table for under addition modulo 6 can be given as follows:

(3) We need to construct Cayley’s table for under multiplication modulo 3.

Here,

Hence, Cayley’s table for under multiplication modulo 3 can be given as follows:

(4) We need to construct Cayley’s table for under multiplication modulo 4.

Here,

Hence, Cayley’s table for under multiplication modulo 4 can be given as follows:

(5) We need to construct Cayley’s table forunder addition modulo 10.

Here,

Hence, the required Cayley’s table is:

(6) We need to construct Cayley’s table forunder multiplication modulo 12.

Here,

Hence, the required Cayley’s table is: