Question

To determine the interpretation of the equivalence classes for the equivalence relation \(R\).

Short answer

Same value.

Step-by-step solution

Given data

Given data is String \( = (1,2)\).

Formula used of equivalence relation

The equivalence relation is\((a,b),(c,d) \in R\)if and only if\(ad = bc\).

Also, rewrite it as:

\((a,b),(c,d) \in R{\rm{ if and only if }}\frac{a}{b} = \frac{c}{d}{\rm{. }}\)

Find equivalence classes

Each equivalence class follows all values of \((p,q)\), as fractions. Also, these have the same value (likewise, the same element of \({Q^ + }\)).