Let A = {0, 1, 2, 3, 4, 5}. Let R be a relati | vedclass

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(C) The set is $A = \{0, 1, 2, 3, 4, 5\}$. The relation $R$ is defined by $(x, y) \in R$ if $\max\{x, y\} \in \{3, 4\}$.We list the pairs $(x, y)$ suc

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only $(S_2)$ is true

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(C) The set is $A = \{0, 1, 2, 3, 4, 5\}$. The relation $R$ is defined by $(x, y) \in R$ if $\max\{x, y\} \in \{3, 4\}$.We list the pairs $(x, y)$ such that $\max\{x, y\} = 3$ or $\max\{x, y\} = 4$:For $\max\{x, y\} = 3$,the pairs are $(0, 3), (3, 0), (1, 3), (3, 1), (2, 3), (3, 2), (3, 3)$.For $\max\{x, y\} = 4$,the pairs are $(0, 4), (4, 0), (1, 4), (4, 1), (2, 4), (4, 2), (3, 4), (4, 3), (4, 4)$.The set $R = \{(0, 3), (3, 0), (1, 3), (3, 1), (2, 3), (3, 2), (3, 3), (0, 4), (4, 0), (1, 4), (4, 1), (2, 4), (4, 2), (3, 4), (4, 3), (4, 4)\}$.The number of elements in $R$ is $16$. Thus,$(S_1)$ is false.For reflexivity: $(0, 0) 
otin R$ since $\max\{0, 0\} = 0 
otin \{3, 4\}$. Thus,$R$ is not reflexive.For symmetry: If $(x, y) \in R$,then $\max\{x, y\} \in \{3, 4\}$. Since $\max\{x, y\} = \max\{y, x\}$,it follows that $(y, x) \in R$. Thus,$R$ is symmetric.For transitivity: $(0, 3) \in R$ and $(3, 1) \in R$,but $(0, 1) 
otin R$ because $\max\{0, 1\} = 1 
otin \{3, 4\}$. Thus,$R$ is not transitive.Therefore,$(S_2)$ is true.

Let $A = \{0, 1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$. Then among the statements $(S_1)$: The number of elements in $R$ is $18$,and $(S_2)$: The relation $R$ is symmetric but neither reflexive nor transitive:

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