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  • Determine whether each of the following relations are reflexive, symmetric and transitive: (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}

1. Determine whether each of the following relations are reflexive, symmetric and
transitive:

(iii) Relation R in the set A = \{1,2,3,4,5,6\} as R = \{(x,y) : y \; \textup{is} \; divisible \; by\; x\}

Answers (1)

best_answer

A = \{1,2,3,4,5,6\}

R = \left \{ \left ( 2,4 \right ),\left ( 3,6 \right ),\left ( 2,6 \right ),\left ( 1,1 \right ),\left ( 2,2 \right ),\left ( 3,3 \right ),\left ( 4,4 \right ),\left ( 5,5 \right ),\left ( 6,6 \right )\right \}

Any number is divisible by itself  and  \left ( x,x \right ) \in R.So it is reflexive.

\left ( 2,4 \right ) \in R but \left ( 4,2 \right ) \notin R . Hence, it is not symmetric.

\left ( 2,4 \right ),\left ( 4,4 \right ) \in R and  4 is divisible by 2, and 4 is divisible by 4. Hence, it is transitive.

Hence, it is reflexive and transitive but not symmetric.

 

 

 

 

Posted by

seema garhwal

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