Question

If set A has 5 elements and set B has 7 elements than number of one-one and onto mapping from A to B is:

• A. 2
• B. 0
• C. 1
• D. 3

Answer 1

The Correct Option is B

To determine the number of one-to-one and onto mappings (bijections) from set A to set B, we must first understand the requirements for such a mapping. A mapping is one-to-one (injective) if each element in the domain maps to a unique element in the codomain. It is onto (surjective) if every element in the codomain has a preimage in the domain.

Given set A has 5 elements and set B has 7 elements, an onto mapping requires the codomain to be equal in size to or smaller than the domain. Therefore, it is impossible to map every element of B to an element in A in a one-to-one, onto fashion because there are fewer elements in set A (5) than in set B (7).

For a function to be both one-to-one and onto, the sets must have the same cardinality, which in this case, they do not. Therefore, the number of one-to-one and onto mappings from set A to set B is 0.