Answer to Question #131438 in Discrete Mathematics for jaya

Question

(i) Determine whether each of these functions from [a,b,c,d] to itself is one-to-one.
(a) f(a) = b, f(b) = a, f(c) = c, f(d) =d
(b) f(a) = b, f(b) = b, f(c) = d, f(d) = c
(c) f(a) = d, f(b) = b, f(c) = c, f(d) = d
(ii) Which functions in part (i) are onto?

Answer 1

A function $f:A\rightarrow B$ is said to be one-one if different elements in $A$ have different images in $B$ . In symbols,

$x_1\neq x_2 \implies f(x_1)\neq f(x_2); \ where x_1,x_2 \in A$

$f$ is called onto if $f(A)=B$ i,e each elements in $B$ is the functional image of at least one element of $A$ .

1) Answer: (a) one-one

(b) not one-one

(c) not one-one

2) answer: only (a) is onto.