Question

Q51. Let e = {1, 2, 3, 4} and f = {1, 2} .Then the number of onto functions from e to f is

Answer 1

Given ,

e = {1, 2, 3, 4}

f = {1, 2}

Number of terms of set e , n(e) = 4

Number of terms of set f , n(f) = 2

We know that ,

$\pink{ \large \fbox{ \sf \fbox{No. \: of \: function \: or \: relations = No. \: of \: subsets \: of \: e × f}}}$

So ,

$\sf n(e \times f) = n(e) \times n(f) \\ \\ \sf n(e \times f) =4 \times 2 \\ \\ \sf n(e \times f) =8$

Thus , the subsets of e × f is $\sf {(2)}^{8} \: \: i.e \: \: 256$

Therefore , the no. of functions is 256