

Set Theory

Here You can find
1. Union
2. Intersection
3. Complement
4. Proper Subsets
5. Minus
6. Cross Product
7. Prove that any two expression is equal or not

1.
Union

(1) A = {1,2,3,4,5}, B = {3,4,5,6} Find A U B ...
Here `A = {1,2,3,4,5}, B = {3,4,5,6}`
`A uu B = {1,2,3,4,5} uu {3,4,5,6}`
`= {1,2,3,4,5,6}`


2.
Intersection

(1) A = {1,2,3,4,5}, B = {3,4,5,6} Find A n B ...
Here `A = {1,2,3,4,5}, B = {3,4,5,6}`
`A nn B = {1,2,3,4,5} nn {3,4,5,6}`
`= {3,4,5}`



3.
Complement

(1) U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5} Find A' ...
Here `U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}`
`A' = {1,2,3,4,5}'`
`= {6,7,8,9,10}`


4.
Proper Subsets

(1) C = {7,8,9} Find Proper subset of C ...
Here `C = {7,8,9}`
`P(C) = {{7},{8},{9},{7,8},{7,9},{8,9},{7,8,9}}`



5.
Minus

(1) A = {1,2,3,4,5}, B = {3,4,5,6} Find A  B ...
Here `A = {1,2,3,4,5}, B = {3,4,5,6}`
`A  B = {1,2,3,4,5}  {3,4,5,6}`
`= {1,2}`


6.
Cross Product

(1) A = {1,2,3}, B = {4,5} Find A × B ...
Here `A = {1,2,3}, B = {4,5}`
`A × B = {1,2,3} × {4,5}`
`= { (1,4), (1,5), (2,4), (2,5), (3,4), (3,5) }`



7.
Prove that any two expression is equal or not

A = {1,2,3,4,5}, B = {3,4,5,6}, C = {7,8,9}, Prove that A U (B U C) = (A U B) U C ...
Here `A={1,2,3,4,5},B={3,4,5,6},C={7,8,9}`
To find LHS = `(A uu B) uu C`
`A uu B = {1,2,3,4,5} uu {3,4,5,6}`
`= {1,2,3,4,5,6}`
`(A uu B) uu C = {1,2,3,4,5,6} uu {7,8,9}`
`= {1,2,3,4,5,6,7,8,9}`
`:. (A uu B) uu C = {1,2,3,4,5,6,7,8,9} >(1)`
To find RHS = `A uu (B uu C)`
`B uu C = {3,4,5,6} uu {7,8,9}`
`= {3,4,5,6,7,8,9}`
`A uu (B uu C) = {1,2,3,4,5} uu {3,4,5,6,7,8,9}`
`= {1,2,3,4,5,6,7,8,9}`
`:. A uu (B uu C) = {1,2,3,4,5,6,7,8,9} >(2)`
From (1) and (2) `:. (A uu B) uu C = A uu (B uu C)` (proved)







