If * is a binary operation on A = {1, 2, 3, 4, 5} given by the table shown below:

*

1

2

3

4

5

1

1

1

1

1

1

2

1

2

1

2

1

3

1

1

3

1

1

4

1

2

1

4

1

5

1

1

1

1

5

Find the value of (3 * 3) * (4 * 4) ?

Question

Question

Answer 1

Concept:

An operation * on a non-empty set S, is said to be a binary operation if it satisfies the closure property.

Closure Property:

Let S be a non-empty set and a, b ∈ S, if a * b ∈ S for all a, b ∈ S then S is said to be closed with respect to operation *.

Calculation:

Given: * is a binary operation on A = {1, 2, 3, 4, 5} given by the table shown below:

Here we have to find the value of (3 * 3) * (4 * 4)

⇒ (3 * 3) = 3 and (4 * 4) = 4-----------(from the table given above)

⇒ (3 * 3) * (4 * 4) = 3 * 4 = 1-----------(From the table given above)