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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 - Mathematics and Statistics

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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

Sum
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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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Chapter 5: Sets and Relations - Exercise 5.2 [Page 103]

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