Question

If $A=\{a,b,c,d,e\}$ and $B=\{1,2,3\}$, then the total number of non-empty relations from $A$ to $B$ is

• A. $5^3-1$
• B. $3^5-1$
• C. $2^{3\times 5}-1$
• D. $3\times 5-1$

Answer 1

The correct option is C $2^{3\times 5}-1$

Total number of relations $=2^{3\times 5}$, which contains empty set too.
$\therefore$ Total number of non-empty relations from $A$ to $B$ will be $2^{15}-1$