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  1. Tardigrade
  2. Question
  3. Mathematics
  4. Let X and Y be two non-empty sets. Let f: X arrow Y be a function. For A ⊂ X and B ⊂ Y, define f(A)= f(x): x ∈ A ; f-1(B)= x ∈ X: f(x) ∈ B then

Q. Let and be two non-empty sets. Let be a function. For and , define , then

Relations and Functions - Part 2 Report Error

Solution:





Now if
It may happen that does not Exist in as function is not given to be subjective.

Also, but

From above, we can't conclude
If the function is non-injective,
then it may happen that and .

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4. Let be the real line consider the following subsets of the plane
and
is an integer
which of the following is true ?

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5. The number of bijective functions from the set to itself, if contains elements is -

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