no. of functions

Question

The number of function from set {1, 2, 3, 4, 5, 6, 7, 8} to set {0, 1} such that assign 1 to exactly one of given number less than 8 are .......................

Comments

8 functions are possible.

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????????????

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@Anu sir,

I'm not sure :p

Answer 1

Let's assume $1$ in Range is assigned to $2$ in domain. Then we have the requirement for a function that every element in the domain should have an image. So, for $1,3,4,5,6,7,8$ we need images. All the numbers can only be assigned to $0$ since the questions says $1$ is mapped to exactly one element in the domain.

So, for the preimage of $1$ we have $7$ choices and after selecting it we have to assign all remaining elements in domain to $0$. Thus $7$ functions are possible.

Edit: If $8$ is free to choose from $0$ or $1$ then $7$ ways to choose one element from $\{1,2,3,4,5,6,7\}$ and $8$ can map to $0$ or $1$ making the final answer as $7*2 =14$

Comments

ans given for this question is 14.

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there is no restriction on 8.

Question says if no. < 8 then exactly one will connect to it but 8 can connect to 0 or 1.

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It depends on the way you interpret it. The words aren't properly phrased to make out a definite meaning. I guess yours is a possible interpretation too. Thank you :)