A ∪ B ∪ C | = | A| + | B | + |C | -(| A ∩B ) | (B ∩ C )- (C ∩ A)+ ( A ∩ B ∩ C )
Where A = {1, 2, 3, 4, 5}, B = {2, 3, 4, 6}, C = {3, 4, 6, 8}
Answers
Answer:
sorry I don't anderstand your questions
Answer:
The question is wrong. I dont know where this question came from, but it's being circulated and it makes no sense.
The question is:
Verify:
| A ∪ B ∪ C | = | A| + | B | + |C | - |A ∩ B| - |B ∩ C|- |C ∩ A|+ | A ∩ B ∩ C |
Where A = {1, 2, 3, 4, 5}, B = {2, 3, 4, 6}, C = {3, 4, 6, 8}
Step-by-step explanation:
|A| is the cardinality of a set. It is basically the number of elements in the set.
So, in this question:
(A ∪ B ∪ C) = {1, 2, 3, 4, 5, 6, 8}
So, | A ∪ B ∪ C | = 7
A = {1, 2, 3, 4, 5}
| A| = 5
B = {2, 3, 4, 6}
| B | = 4
C = {3, 4, 6, 8}
|C | = 3
(A ∩ B) = {2,3,4}
|A ∩ B| = 3
(B ∩ C) = {3,4}
|B ∩ C| = 2
(C ∩ A) = {3,4}
|C ∩ A| = 2
( A ∩ B ∩ C ) = {3,4}
| A ∩ B ∩ C | = 2
Substitute, LHS and RHS,
| A ∪ B ∪ C | = | A| + | B | + |C | - |A ∩ B| - |B ∩ C|- |C ∩ A|+ | A ∩ B ∩ C |
7 = 5 + 4 + 3 - 3 - 2 - 2 + 2
7 = 7
LHS=RHS
hence, verified