Intuitive Math

Intuitive Math: (By observation)
Let Set I = {(x,y)| x,y∈ R}
Set O = {(x,y)| (y-3 / x-2) = 1}
Set E = {(x,y)| y ≠ x+1}
Let A = O U E (union of O and E)
Find: Ā ?
Solution:
By Intuition:
Let I be a blackboard
O be the straight line (x≠2, y≠3):
y-3 / x-2 = 1
y -3 = x -2
y= x+1 exclude point (2,3)
E the straight line y=x+1
Ō = remove the straight line but keep (2,3)
Ē = remove the straight line
Ā = Ō ∩ Ē  = {(2,3)}
[QED]
Verify:
O={(x,y) | x≠2, y≠3,  y= x+1}
=> Ō= {(x,y) | x=2,y=3}
Ē={(x,y)| y= x+1}
Ā= Ō ∩ Ē  = {(2,3)}    [QED]
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