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# Let a = (3, 5) and B = (7, 11). Let R = {(A, B) : a ∈ A, B ∈ B, a − B is Odd}. Show that R is an Empty Relation from a into B. - Mathematics

Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

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#### Solution

Given:
A = (3, 5) and B = (7, 11)
Also,
R = {(ab) : a ∈ A, b ∈ B, a − b is odd}
a are the elements of A and b are the elements of B.

$\therefore a - b = 3 - 7, 3 - 11, 5 - 7, 5 - 11$
$\Rightarrow a - b = - 4, - 8, - 2, - 6$
$\text{ Here, a - b is always an even number} .$

So, R is an empty relation from A to B.
Hence proved.

Concept: Relation
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.3 | Q 7 | Page 21
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