Q. 354.0( 3 Votes )
If the set A cont A. 720
D. none of these
Number of elements in A = 5
Number of elements in B = 6
Now, for a function to be one-one all elements of domain should have unique image in co-domain.
Here, 5 elements of A can be mapped to 5 distinct element of B.
⇒ function is one-one
But range of B is 6 that means there is one element in B which does not have pre-image in A.
Thus the function cannot be onto if it is one-one.
Also, if all 6 elements of B are mapped to all 5 elements of A, then we can observe there will be atleast 2 elements of B which have same pre-image in A.
⇒ one element of A will have two image in B.
⇒ function is not one-one
Thus the function cannot be one-one if it is onto.
Hence, there cannot be any one-one and onto mapping from A to B.
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