Question

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

• A. \(9\)
• B. \(12\)
• C. \(64\)
• D. none of these

Hint:

Number of functions from an \(m\)-element set to an \(n\)-element set is \(n^{m}\).

Answer 1

The Correct Option is A

For a function \(f:A\to B\), each element of \(A\) may be sent to any element of \(B\). Here \(|A|=2\), \(|B|=3\). For the first element of \(A\) there are \(3\) choices; for the second, again \(3\) choices (independent). Thus total functions \(=3\times3=3^{2}=9\).