Define the relation R in the set `N xx N` as follow :
For `(a,b), (c,d) in N xx N, (a,b) R (c,d)` iff ad = bc.
Prove that R is an equivalence relation in `N xx N`

Let ~ be a relation defined on N xx N as follows: (a,b),(c,d) in N xx N, (a,b) ~ (c,d) if ad = bc, then

Let Z be the set of all integers and Z_(0) be the set of all non-zero integers.Let a relation R on Z xx Z_(0) be defined as follows: (a,b)R(c,d)hArr ad=bc for all (a,b),(c,d)in Z xx Z_(0) Prove that R is an equivalence relation on Z xx Z_(0)

Let N be the set of all natural numbers and let R be a relation on N xx N, defined by (a,b)R(c,d)ad=bc for all (a,b),(c,d)in N xx N. Show that R is an equivalence relation on N xx N. Also,find the equivalence class [(2,6)].

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The union of two equivalence relations is an equivalence relation.

Let A={1,2,3,......, 12} and R be a relation in A xx A defined by (a, b) R (c,d) if ad=bc AA(a,b),(c,d) in A xx A . Prove that R is an equivalence relation. Also obtain the equivalence class [(3,4)] .

Prove that a relation R defined on N xx N where (a,b)R(c,d)hArr ad=bc is an equivalence relation.