Q. 36

# Let A = {1, 2, 3, A. nP^{2}

B. 2^{n} – 2

C. 2^{n} – 1

D. None of these

Answer :

Given that, A = {1, 2, 3, ...n} and B = {a, b}

Number of elements in A = n

Number of elements in B = 2

No. of possible function from A → B is n^{2} (i.e. number of possible ways n elements of A can be mapped to 2 elements of B.

Now, not all of these functions are surjective.

we know that function f : A → B is surjective if both the elements of B are mapped.

Out of these n^{2} functions there will be two functions where all the elements of A are mapped to first element of B and where all the elements of A are mapped to second element of B, those functions are not surjective.

⇒ number of surjective functions from A → B are n^{2} – 2.

Rate this question :

Fill in theMathematics - Exemplar

Let f : [2, ∞) <sMathematics - Exemplar

Let f : N →Mathematics - Exemplar

Fill in theMathematics - Exemplar

Let f :R →<Mathematics - Exemplar

Let f : [0, 1] <sMathematics - Exemplar

Which of the follMathematics - Exemplar