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Question
Let A = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation
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Solution
a ∈ A and b ∈ B
∴ a is even and b is odd
∴ a − b is odd
Hence, there is no element in R1, i.e., R1 is an empty relation from A to B.
If a ∈ A, b ∈ B, a is even and b is odd
∴ a + b is always odd
∴ (a, b) ∈ R2 for all a ∈ A, b ∈ B
∴ R2 is an universal relation
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