If R is a relation on the set N (set of natur | vedclass

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(C) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(x, y) \in N 	imes N : 3x + 3y = 10\}$.$1$. Check for Reflexivity: For $R

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$TFT$

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(C) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(x, y) \in N 	imes N : 3x + 3y = 10\}$.$1$. Check for Reflexivity: For $R$ to be reflexive,$(x, x) \in R$ for all $x \in N$. This implies $3x + 3x = 10$,so $6x = 10$,which gives $x = 10/6 = 5/3$. Since $5/3 
otin N$,the relation is not reflexive. Statement-$2$ is $F$.$2$. Check for Symmetry: For $R$ to be symmetric,if $(x, y) \in R$,then $(y, x) \in R$. If $3x + 3y = 10$,then $3y + 3x = 10$. Thus,if $(x, y) \in R$,then $(y, x) \in R$. Since there are no elements $(x, y)$ in $N 	imes N$ satisfying $3x + 3y = 10$,the relation $R$ is the empty set $\phi$. The empty relation is vacuously symmetric. Statement-$1$ is $T$.$3$. Check for Transitivity: For $R$ to be transitive,if $(x, y) \in R$ and $(y, z) \in R$,then $(x, z) \in R$. Since $R = \phi$,there are no pairs $(x, y)$ and $(y, z)$ such that $(x, y) \in R$ and $(y, z) \in R$. Therefore,the condition for transitivity is vacuously satisfied. Statement-$3$ is $T$.Thus,the sequence is $TFT$.

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