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Let R Be a Relation From N To N Defined by R = {(A, B): A, B ∈ N And A = B2}. Are the Following True? - CBSE (Arts) Class 11 - Mathematics

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Question

Let R be a relation from N to N defined by R = {(ab): ab ∈ N and a = b2}. Are the following true?

(i) (aa) ∈ R, for all a ∈ N

(ii) (ab) ∈ R, implies (ba) ∈ R

(iii) (ab) ∈ R, (bc) ∈ R implies (ac) ∈ R.

Justify your answer in each case.

Solution

R = {(ab): ab ∈ N and a = b2}

(i) It can be seen that 2 ∈ N;however, 2 ≠ 22 = 4.

Therefore, the statement “(aa) ∈ R, for all a ∈ N” is not true.

(ii) It can be seen that (9, 3) ∈ N because 9, 3 ∈ N and 9 = 32.

Now, 3 ≠ 92 = 81; therefore, (3, 9) ∉ N

Therefore, the statement “(ab) ∈ R, implies (ba) ∈ R” is not true.

(iii) It can be seen that (16, 4) ∈ R, (4, 2) ∈ R because 16, 4, 2 ∈ N and 16 = 42 and 4 = 22.

Now, 16 ≠ 22 = 4; therefore, (16, 2) ∉ N

Therefore, the statement “(ab) ∈ R, (bc) ∈ R implies (ac) ∈ R” is not true.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 2: Relations and Functions
Ex. 2.40 | Q: 9 | Page no. 46

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Solution Let R Be a Relation From N To N Defined by R = {(A, B): A, B ∈ N And A = B2}. Are the Following True? Concept: Algebra of Real Functions.
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