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Let A and B be two sets having m an...

Let A and B be two sets having m and n elements respectively . Then total number of functions from A to B is

A

219

B

256

C

275

D

510

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `n(A) = 4 , n(B)=2 rArr n(A xx B) =8`
Total number of subsets of set `(A xx B)= 2^(8)`
Number of subsets of set `A xx B ` having no element `(i.e. Phi) = 1.`
Number of subsets of set `A xx B` having one element `= "" ^(8)C_(1)`
Number of subsets of set ` A xx B ` having two elements `= "" ^(8)C_(2)`
` therefore ` Number of subsets having alteast three elements
`=2^(8)-(1+"" ^(8)C_(1)+"" ^(8)C_(2))=2^(8)-1-8-28`
`=2^(8)-37=256-37=219`
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