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Set
Exercise 9 - Example(Page 1) 		Home
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Set Difference:
Set difference: The difference of two sets A and B is given by A-B. A-B is the set of elements that belong to A but do not belong to B.
Symmetric difference between any two sets A and B is given as:
A D B = (A - B) (B - A)


Properties of Set Operations:
Union and Intersection of sets (Commutative property):
A B = B A
A B = B A
Example: 1
A = {a,b,c} and B = {c,d,e}
A B = {a,b,c,d,e}
B A = {a,b,c,d,e}
A B = B A
Example: 2
A = {a,b,c} and B = {c,d,e}
A B = {c}
B A = {c}
A B = B A


Union and Intersection of sets (Associative property):
(A B) C = A (B C)
(A B) C = A (B C)
Example: 3
A = {1,2,3}, B = {2,4,6}, C = {1,3,5}
(A B) = {1,2,3,4,6}
(A B) C = {1,2,3,4,5,6}
B C = {1,2,3,4,5,6}
A (B C) = {1,2,3,4,5,6}
(A B) C = A (B C)
Example: 4
A = {1,2,3}, B = {2,4,6}, C = {1,3,4,5}
(A B) = {2}
(A B) C = { }
(B C) = {4}
A (B C) = { }
(A B) C = A (B C)


Difference of sets (Commutative property):
(A - B) (B - A)
Example: 5
A = {1,2,3}, B = {2,4,6},
A - B = {1,3}
B - A = {4,6}
(A - B) (B - C)


Difference of sets (Associative property):
(A - B) - C A - (B - C)
Example: 6
A = {1,2,3}, B = {2,4,6}, C = {1,3,4,5}
(A - B) = {1,3}
(A - B) - C = { }
(B - C) = {2,6}
A - (B - C) = {1,3}
(A - B) - C A - (B - C)


Symmetruc difference of two sets (Commutative property):
A D B = B D A
Example: 7
A = {1,2,3}, B = {2,4,6}
A D B = (A - B) (B - A)
= {1,3} {4,6}
={1,3,4,6}
B D A = (B - A) (A - B)
= {4,6} {1,3}
={1,3,4,6}
A D B = B D A


Symmetric difference of two sets (Associative property):
(A D B) D C = A D (B D C)


Union over Intersection - Distributive property:
A (B C) = (A B) (A C)


Intersection over Union - Distributive property:
A (B C) = (A B) (A C)


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