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Question
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.
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Solution
Given:
A = (3, 5) and B = (7, 11)
Also,
R = {(a, b) : 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.
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