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.

Answer :

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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