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:

Interest

The cost of borrowing money or the payment received for lending money, usually expressed as an annual percentage of the principal amount.

Simple Interest

A way of calculating interest where the interest charge is based on the original principal only and does not compound.

Repaid

The action of paying back borrowed money to a lender, either in installments or as a lump sum.

Loans

Sums of money borrowed that are expected to be paid back with interest, often under agreed-upon terms between lenders and borrowers.