For a Function f : A → B such that n(A) = a, n(B) = b (a,b∈N) then which of the following statements must be CORRECT ?

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For a Function f : A  B such that n(A) = a, n(B) = b (a,bN) then which of the following statements must be CORRECT ?

(A) If function is one - one, onto, then a>b

(B) If function is one - one, into, then a<b

(C) If function is many - one, onto, then a>b

(D) If function is many - one, into, then a<b

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Correct option   (B)(C)

Explanation:

(A) If function is one- one & onto then a = b since every element of set B should have exactly one pre-image in A.
(B) For one - one, into function, every element of set B should have either one pre-image or no pre-image in set A.
⇒ no. of elements in set B > no. of elements in A.
∴ b > a
(C) For many - one, onto function, every element of set B should have one or more than one pre-images in
A.  ⇒ n
(B) < n (A)
⇒ b < a or a > b
(D) For many - one, into function a ∈ R & b ∈ R.