Define a relation $T$ on $\mathbf { R }$ as follows: for all $x$ and $y$ in $\mathbf { R } , x T y$ if and only if $x ^ { 2 } = y ^ { 2 }$. Then $T$ is an equivalence relation on $\mathbf { R }$.
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.

Question

Define a relation $T$ on $\mathbf { R }$ as follows: for all $x$ and $y$ in $\mathbf { R } , x T y$ if and only if $x ^ { 2 } = y ^ { 2 }$. Then $T$ is an equivalence relation on $\mathbf { R }$. 
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.

Quizplus · Accepted Answer

The Answer of Define a relation $T$ on $\mathbf { R }$ as follows: for all $x$ and $y$ in $\mathbf { R } , x T y$ if and only if $x ^ { 2 } = y ^ { 2 }$. Then $T$ is an equivalence relation on $\mathbf { R }$. 
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.

Define a Relation TTT On R\mathbf { R }R As Follows: for All

Define a Relation $T$ On $\mathbf { R }$ As Follows: for All