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]