1.

How many of the functions Suppose A is a set of n elements and B is a set with m elementsare one - one with (i)m=n ,(ii) m < n, (iii) m>n

Answer»

Solution :"We have" `|A|=n,|B|=m`
`:.` "The number of one-one FUNCTIONS from"
`"A to B is" ""^mP_n=(m!)/((m-n)!) "When "m gt n.`
`"if "m=n,"the number of one-one functions is "(m!)/((m-m)!)=(m!)/(0!)=m! =n!`
`"If" m LT n," then there is no POSSIBILITY of one-one functions".


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