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#### playboy

##### Guest

Let S be the Cartesian coodinate plane R x R 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)

....So i want to show that the 3 properties of an equivalence reltion holds: (reflective propery, symmetric propery and transitive propery.)

**1. reflective propery**

(a,b)=(a,b) and (c,d)=(c,d)......(not hard)

**2. symmetric propery**

Let (a,b) be in A and (c,d) be in B and if A R B, then (a,b) = (c,d)

so, (c,d) = (a,b) and thus, B R A.

How does that sound?

**3. transitive propery**

i have no idea how to start this

i mean, the property states "if xRy and yRz, then xRz"

so will this work:?

if (a,b)=(c,d) and (c,d)=(e,f), then (a,b)=(e,f)

but then i feel like i making things up when i put in (e,f)?