. Set A has 3 elements and set B has 4 elements


The number of injections that can be defined from A into B is :

A: 144

B: 12

C: 24

D: 64

 

Best Answer

Explanation:-

In this question,given a number of elements of two sets A and B and to find the number of injections that can be defined from A to B. 

This means to find the number of one-one functions from A into B.

For this, first understand one one function and how to use them. After that, find a number of ways function can be defined.

Injections are functions that map distinct elements of its domain to distinct elements of its codomain 

To define injective function from set A to B, map the first element of set A to any of the 4 elements of set B. 

the second element cannot be mapped to the same element of set A,  there are three choices in set B for the second element of set A. 

Similarly, there are two choices in set B for third elements of set A.

From all this, we conclude that, total number of injection from set A to set B are 

4×3×2=24

The total injections from set A into set B are 24.

 

Correct Option is: (C)

Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A into B is 24.

 

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