Short Answer TypeLet R be the relation in the set {1. 2, 3, 4} given by R = {(1,2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
Choose the correct answer.
(A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.
L.et A be the set of all 50 students of class X in a school. Let f : A → N be function defined by f (x) = roll number of student x. Show that f is one-one but not onto.
Long Answer TypeCheck the injectivity and surjectivity of the following functions :
(i) f : N → N given by f (x) = x2
(ii) f : Z → Z given by f (x) = x2
(iii) f : R → R given by f (x) = x2 (iv) f : N → N given by f (x) = x3
(v) f : Z → Z given by f (x) = x3
Short Answer TypeHere f(x) = x2 Df = R Now 1,–1 ∈ R Also f (1)= 1, f (–1) = 1 Now 1 ≠ –1 but f (1) = f (–1)
∴ f is not one-to-one.
Again, the element – 2 in the co-domain of R is not image of any element x in the domain R.
∴ f is not onto.
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