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  • The relation <img alt="R=\left \{ \left ( a,a \right ),\left ( b,b \right ),\left ( c,c \right ),\left ( a,b \right ),\left ( b,c \right ),\left ( a,c \right )\right \}" src="https://entr

The relation

R=\left \{ \left ( a,a \right ),\left ( b,b \right ),\left ( c,c \right ),\left ( a,b \right ),\left ( b,c \right ),\left ( a,c \right )\right \}

on the set A=\left \{ a,b,c \right \} is

 

Option: 1

Reflexive but not symmetric
 


Option: 2

Reflexive but not transitive
 


Option: 3

Symmetric and transitive
 


Option: 4

Neither symmetric nor transitive


Answers (1)

best_answer

R=\left \{ \left ( a,a \right ),\left ( b,b \right ),\left ( c,c \right ),\left ( a,b \right ),\left ( b,c \right ),\left ( a,c \right )\right \}

Set A=\left \{ a,b,c \right \}

for reflexive R=\left \{ \left ( a,a \right ),\left ( b,b \right ),\left ( c,c \right )\right \}

so given relation is reflexive

Symmetric

R=\left \{ \left ( a,b \right ),\left ( b,a \right ),\left ( a,c \right ),\left ( c,a \right ),\left ( b,c \right ),\left ( c,b \right )\right \}

So given relation is not reflexive

Transitive

R=\left \{ \left ( a,b \right ),\left ( b,a \right ),\left ( a,c \right )\right \}

So given relation is transitive.

Posted by

Gaurav

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