MadeEasy Subject Test: Engineering Mathematics - Functions

Question

Hi Guys,

I think answer should be (D) part because it is not mentioned that function is s Injective. What is your opinion ?

Comments

Hi Ashwani Kumar 2 ji,

Total no of functions from A to B are $n^{m}$

I think correct answer is ${(n+1)}^m$

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@ Chhotu ji 

See, set A has m elements and set B has n elements, function says an element in A should be related to exactly one element in set B and and no element in A should be left empty

So now for every element in set A we have n choices to map a single element and every unique mapping you got gives you a unique function.

Total possible choices are  n*n*n*n.....m times = n^m choices or functions.

You can see this for more reference.

https://math.stackexchange.com/questions/223240/how-many-distinct-functions-can-be-defined-from-set-a-to-b

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Option (c) is correct 

X contains kn elements and W contains 2^kn elements. So to map each element from X to W ... X have 2^kn choices for each element of X.... So 2^kn  * 2^kn  *2^kn  *2^kn  *2^kn  *2^kn  *2^kn  *..... kn time = 2^{(kn )kn}