Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
f: A × B → B × A is defined as f(a, b) = (b, a).
.
∴ f is one-one.
Now, let (b, a) ∈ B × A be any element.
Then, there exists (a, b) ∈A × B such that f(a, b) = (b, a). [By definition of f]
∴ f is onto.
Hence,f is bijective.
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(iv) Reflexive and transitive but not symmetric.
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(v) Relation R in the set A of human beings in a town at a particular time given by
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(b) R = {(x, y): x and y live in the same locality}
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