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# Let A = {1,2,3}, B = {4,5,6,7} and let f = {(1,4), (2,5), (3,6)} be a function from A to B. State whether f is one-one or not.

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Toolbox:
• A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
• A function$f : X \rightarrow Y$ is said to be onto or surjective, if every element of Y is the image of some element of X under f, i.e., for every $y \in Y$, there exists an element x in X such that $f(x) = y$.
Given $A=\{1,2,3\} \qquad B=\{4,5,6,7\}$
Step1: Injective or One-One function:
and f is defined by $f=\{(1,4), (2,5),(3,6)\}$
we see that
$f(1)=4 \qquad f(2)=5 \qquad f(3)=6$
elements 1,2,3 $\in A$ all have district images.
Solution:Therefore $f=\{(1,4), (2,5),(3,6)\}$ is one-one

answered Mar 29, 2013 by