Let S be the Cartesian coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation and describe the equivalence class E(7,3).
you must show three things. R is reflexive, symmetric and transitive
(a) Reflexive: you must show that $\displaystyle (a,b)R(a,b)$ for all $\displaystyle (a,b) \in \mathbb{R} \times \mathbb{R}$
(b) Symmetric: you must show that $\displaystyle (a,b)R(c,d) \implies (c,d)R(a,b)$ for $\displaystyle (a,b), (c,d) \in \mathbb{R} \times \mathbb{R}$
(c) Transitive: you must show that $\displaystyle \Bigg[ (a,b)R(c,d) \mbox{ and } (c,d)R(e,f) \Bigg] \implies (a,b)R(e,f)$ for $\displaystyle (a,b), (c,d), (e,f) \in \mathbb{R} \times \mathbb{R}$
can you do that?
what do you mean E(7,3)? you mean the equivalence class that has the point (7,3) in it?and describe the equivalence class E(7,3).