Let′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a ′ b = H.C.F. of a and b. Is the operation ′ same as the operation defined in Exercise 4 above? Justify your answer.

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Solution

The binary operation ′ on the set {1, 2, 3 4, 5} is defined as a ′ b = H.C.F of a and b.

The operation table for the operation ′ can be given as:

′

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

We observe that the operation tables for the operations * and ′ are the same.

Thus, the operation ′ is same as the operation*.

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Similar questions

Q. Let * ′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a * ′ b = H.C.F. of a and b . Is the operation * ′ same as the operation * defined in Exercise 4 above? Justify your answer.

Q. Let

*^{'}

be the binary operation on the set

{1, 2, 3, 4, 5}

defined by

a *^{'} b = H . C . F .

a

and

b

. Is the operation

*^{'}

s a m e a s t h e o p e r a t i o n

\ast$ defined in above? Justify your answer

Let $*$ be the binary operation of the set {1,2,3,4,5} defined by $a * b = H C F$ of a and b. Is the operation $*$ is same as the operation $*$ defined in Q.4 above? Justify your answer.

Q. Let

*

be an operation such that

a * b =

LCM of

a

and

b

defined on the set

A = {1, 2, 3, 4, 5}

. Is

*

a binary operation? Justify your answer.

Is * defined on the set {1, 2, 3, 4, 5} by a * b = L.C.M. of a and b a binary operation? Justify your answer.

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*′	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

Let*′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a *′ b = H.C.F. of a and b. Is the operation *′ same as the operation * defined in Exercise 4 above? Justify your answer.

Let′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a ′ b = H.C.F. of a and b. Is the operation ′ same as the operation defined in Exercise 4 above? Justify your answer.