Question

If A ={1, 2,3} then the number of reflexive relations in A is ............................... .
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Answer 1

If A = { 1 , 2 , 3 } then the number of reflexive relations in A is 64

Given :

The set A = { 1 , 2 , 3 }

To find :

The number of reflexive relations in A

Concept :

If a set A has n elements, then total number of reflexive relations $\displaystyle \sf{ = {2}^{ {n}^{2} - n} }$

Solution :

Step 1 of 2 :

Write down the number of elements in A

Here the given set is A = { 1 , 2 , 3 }

Number of elements in A = n = 3

Step 2 of 2 :

Find number of reflexive relations in A

We know that if a set A has n elements, then total number of reflexive relations

$\displaystyle \sf{ = {2}^{ {n}^{2} - n} }$

Here by the given n = 3

Hence number of reflexive relations in A

$\displaystyle \sf{ = {2}^{ ({3}^{2} - 3)} }$

$\displaystyle \sf{ = {2}^{ (9 - 3)} }$

$\displaystyle \sf{ = {2}^{ 6} }$

$\displaystyle \sf{ = 64 }$

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Answer 2

Answer:

64

Step-by-step explanation: