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

question 11

Essay

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.

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Definitions:

Decoding

The process by which a receiver interprets and understands a message sent by a sender.

Feedback

In the feedback loop, the sender’s interpretation of the response, which indicates whether a message was decoded and understood as intended during the communication process.

Communication Process

The series of steps through which information is transmitted from one individual or entity to another, typically involving a sender, message, medium, and receiver.

Receiver

In communication, the party who receives and interprets a message sent from a sender.