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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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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 \(B\). Show that \(f\) is one-one.

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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 13, 2013 by thagee.vedartham
edited Mar 20, 2013 by meena.p
 

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