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