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

Explanation

"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".