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.
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.
$\therefore a-b=3-7,3-11,5-7,5-11$
$\Rightarrow a-b=-4,-8,-2,-6$
Here, $a-b$ is always an even number.
So, R is an empty relation from A to B.
Hence proved.
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