A Question on Equivalence relation?

Question

Define a relation ~ on R2 by (x1, y1) ~ (x2, y2) iff x1 = x2

Question:
verify that ~ is an equivalence relation on R2.

Answer 1

In order for ~ to be an equivalence relation, it must satisfy the three properties reflexivity, symmetry, and transitivity. In this case, checking these properties is not so difficult.

Obviously, (x1,y1) = (x1,y1) (reflexivity)

(x1,y1)=(x2,y2) and (x2,y2)=(x1,y1) (symmetry)

and if (x1,y1)=(x2,y2) and (x2,y2)=(x3,y3) , then (x1,y1)=(x3,y3) (transitivity)

note to person above: the relation was defined on R^2 :)

Answer 2

may be incorrect, yet the following is going with equivalence instructions u opt to satisy the three situations, reflesivity it truly is aparent becuase it on addition symetric n +p = m+q transivity then some xRy, yRz then xRz so (m,n) R (p,q) and (p,q) R (a,b) so this suggests, that (m,n) R(a,b) which so m+q = n+p and p+a = q+r so that you decide on to exhibit that m+a = n+b

Answer 3

it is an equivalence relation
x1=x1
x1=x2 then x2=x1
x1=x2 x2=x3 then x1=x3

Answer 4

Reflexive: (x1,y1)~(x1,y1)

Symmetric: (x2,y2)~(x1,y1)

Transitive: (x1,y1)~(x2,y2) and (x2,y2)~(x3,y3)
then clearly, (x1,y2)~(x3,y3)