(i) f : {1, 2, 3, 4} {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)} (ii) g : {5, 6, 7, 8}
(i) f (x) = | x | and g(x) = | 5x – 2 | (ii) f(x) = 8 and g(x)=
(a) f is one-one onto (b) f is many-one onto (c) f is one-one but not onto ...
(a) f is one-one onto (b) f is many-one onto (c) f is one-one but not onto ...
State whether the function f is bijective. Justify your answer.
(i) defined by f(x) = 3-4x (ii) defined by f(x) =
is neither one-one nor onto.
(i) (ii) (iii) (iv) ...
(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.
(i) Symmetric but neither reflexive nor transitive. (ii) Transitive but neither reflexive nor symmetric. (iii) Reflexive and symmetric but not transitive. (iv) Reflexive and transitive but not symmetric. (v) Symmetric and transitive but not reflexive.
(i) R = {(a, b) :|a–b| is a multiple of 4} (ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.