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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 |
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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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