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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. - CBSE (Science) Class 12 - Mathematics

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Question

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

Solution

The binary operation *′ on the set {1, 2, 3 4, 5} is defined as *′ 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*.

 

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 5 | Page no. 25
Solution 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. Concept: Concept of Binary Operations.
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