• Math Archive: Questions from 2023-06-21

    (a) For the relation {(6,6), (6,7), (6,8), (7,6), (7,7), (7,8)} on the set {5,6,7,8}, decide whether it is reflexive, symmetric and transitive or not. (b) For relation R = {(a,b): a,b E A, |a

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    Consider the relation R = (x, y) = R x R : |x

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    Consider the relation R = (x, y) ∈ R × R : x - y ∈ Z on R. Prove that relation R is reflexive and symmetric, and transitive.
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    Prove that the below function is surjective: f : R ---> R, f(x) = x^2

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    Determine whether function f : {N U 0} --> {N U 0} defined by f(x) = {x - 1, x + 1, if x is odd x is even is (a) One-to-one and (b) Onto.
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    Show that the function f(x) = x-2/x-3 defined on f : R - {3} ---> R - {1} is a bijection. for the function to be bijective, function weed to be both injective (one-to-one) & surjective (onto.)

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