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Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1,2,3,...,13,14} defined as R = {(x,y): 3x-y = 0}

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

(i) Relation R in the set A = \{1,2,3 ...,13 ,14\} defined asR = \{(x,y): 3x - y = 0\}

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A = \{1,2,3 ...,13 ,14\}

R = \{(x,y): 3x - y = 0\} = \left \{ \left ( 1,3 \right ),\left ( 2,6 \right ),\left ( 3,9 \right ),\left ( 4,12 \right ) \right \}

Since,  \left ( 1,1 \right ),\left ( 2,2 \right ),\left ( 3,3 \right ),\left ( 4,4 \right ),\left ( 5,5 \right )\cdot \cdot \cdot \cdot \cdot \cdot \left ( 14,14 \right ) \notin R so R is not reflexive.

Since, \left ( 1,3 \right ) \in R but  \left ( 3,1 \right ) \notin R so R is not  symmetric.

Since, \left ( 1,3 \right ),\left ( 3,9 \right ) \in R but \left ( 1,9 \right ) \notin R so R is not  transitive.

Hence, R is neither reflexive nor  symmetric and nor transitive.

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