Q. 45.0( 2 Votes )

# If A = {a, b, c} and B = {–2, –1, 0, 1, 2}, write total number of one-one functions from A to B.

Formula:-

(I)A function is one-one function or an injection if

f(x)=f(y)

x=y for all x, y A

or f(x)f(y)

xy for all x, y A

(II)if A and B are two non-empty finite sets containing m and n

(i) Number of function from A to B = nm

(ii) Number of one–one function from A to B

(iii) Number of one-one and onto function from A to B

(iv) Number of onto function from A to B=

Let f: AB be one-one function

F(a)=3 and f(B)=5

Using formula

Number of one–one function from A to B

3C5.5!=60

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