A Relationship ; mathematically !

Probability Level 4

S = { L , O , V , E , U , { G , O , L , U } } \color{magenta}{S=\{ L,O,V,E,U,\{G,O,L,U \} \}}

A relations R R is defined on the set S \color{magenta}{S} given above. Find the maximum no. of possible Reflexive Relations R R on S \color{magenta}{S} .

2 36 2^{36} 1 2 56 2^{56} 2 8 2^8 2 72 2^{72} None of the given. 2 30 2^{30}

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Rama Devi
Jun 2, 2015

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Sandeep Bhardwaj
May 29, 2015

If any set A has n elements,then the total no of possible Reflexive Relations defined on the set A is ( 2 n 2 − n ) \boxed{\text{ If any set} A \text{ has } n \text{ elements,then the total no of} \\ \text{possible Reflexive Relations defined} \\ \text{on the set } A \ \text{ is } \left( 2^{n^2-n} \right)}

So the given set S \color{magenta}{S} has 6 6 elements. ( What are those 6 elements ?)

So, maximum no. of Reflexive Relations = 2 6 2 − 6 = 2 30 =2^{6^2-6}=\boxed{2^{30}}

enjoy !

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Very nice solution.

Maths Mathematics - 6 years ago

Sir, are there any more formulae for transitive and symmetric relations also. I am preparing for this topic for JEE main 2016. So please help.

Avadhoot Sinkar - 5 years, 3 months ago

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