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Let R Be a Relation on N × N Defined By(A, B) R (C, D) ⇔ A + D = B + C For All (A, B), (C, D) ∈ N × N(Iii) (A, B) R (C, D) and (C, D) R (E, F) ⇒ (A, B) R (E, F) for All (A, B), (C, D), (E, F) ∈ N × N - Mathematics

Let R be a relation on N × N defined by
(ab) R (cd) ⇔ a + d = b + c for all (ab), (cd) ∈ N × N

(iii) (ab) R (cd) and (cd) R (ef) ⇒ (ab) R (ef) for all (ab), (cd), (ef) ∈ N × N

 
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Solution

We are given ,
(ab) R (cd) ⇔ a + d = b + c for all (ab), (cd) ∈ N × N

(iii) (ab) R (cd) \text{ and }  (cd) R (ef) ⇒ (ab) R (ef) for all (ab), (cd), (ef) ∈ N × N

\[(a, b) R (c, d) \text{ and } (c, d) R (e, f)\]
\[ \Rightarrow a + d = b + c \text{ and } c + f = d + e\]
\[ \Rightarrow a + d + c + f = b + c + d + e \]
\[ \Rightarrow a + f = b + e \]
\[ \Rightarrow (a, b) R (e, f)\]

 
Concept: Relation
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.3 | Q 22.3 | Page 21
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