Question

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.

Answer 1

Dear student
$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{A}=\left\{1,2,3\right\},\mathrm{B}=\left\{4,5,6,7\right\} \\ \mathrm{f}:\mathrm{A}\to \mathrm{B}\mathrm{is}\mathrm{defined}\mathrm{as} \\ \mathrm{f}=\left\{\left(1,4\right),\left(2,5\right),\left(3,6\right)\right\} \\ \mathrm{So},\mathrm{f}\left(1\right)=4 \\ \mathrm{f}\left(2\right)=5 \\ \mathrm{f}\left(3\right)=6 \\ \mathrm{It}\mathrm{is}\mathrm{seen}\mathrm{that}\mathrm{the}\mathrm{images}\mathrm{of}\mathrm{distinct}\mathrm{elements}\mathrm{of}\mathrm{A}\mathrm{under}\mathrm{f}\mathrm{are}\mathrm{distinct}. \\ \mathrm{Hence}\mathrm{function}\mathrm{f}\mathrm{is}\mathrm{one}-\mathrm{one}. \end{gathered}$$
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