Consider the following two binary relations on the set $A = \{ a , b , c \} : R _ { 1 } = \{ ( c , a ) , ( b , b ) , ( a , c ) , ( c , c ) , ( b , c ) , ( a , a ) \}$ and $R _ { 2 } = \{ ( a , b ) , ( b , a ) , ( c , c ) , ( c , a ) , ( a , a ) , ( b , b ) , ( a , c ) \}$, then : (1) $R _ { 2 }$ is symmetric but it is not transitive (2) both $R _ { 1 }$ and $R _ { 2 }$ are not symmetric (3) both $R _ { 1 }$ and $R _ { 2 }$ are transitive (4) $R _ { 1 }$ is not symmetric but it is transitive
Consider the following two binary relations on the set\\
$A = \{ a , b , c \} : R _ { 1 } = \{ ( c , a ) , ( b , b ) , ( a , c ) , ( c , c ) , ( b , c ) , ( a , a ) \}$ and\\
$R _ { 2 } = \{ ( a , b ) , ( b , a ) , ( c , c ) , ( c , a ) , ( a , a ) , ( b , b ) , ( a , c ) \}$, then :\\
(1) $R _ { 2 }$ is symmetric but it is not transitive\\
(2) both $R _ { 1 }$ and $R _ { 2 }$ are not symmetric\\
(3) both $R _ { 1 }$ and $R _ { 2 }$ are transitive\\
(4) $R _ { 1 }$ is not symmetric but it is transitive