Question

If \(A=\{a,b\}\), \(B=\{1,2,3\}\) then the total number of one–one (injective) functions from \(A\) to \(B\) is

• A. \(6\)
• B. \(8\)
• C. \(9\)
• D. none of these

Hint:

One–one maps from size \(m\) to size \(n\) (with \(n\ge m\)) are \(nP m=\frac{n!}{(n-m)!}\).

Answer 1

The Correct Option is A

For injective \(f:A\to B\), distinct elements of \(A\) must go to distinct elements of \(B\). Choose an image for \(a\): \(3\) choices. Then for \(b\) only \(2\) choices remain (must be different). Total \(=3\times2=6=P(3,2)\).