Question

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}

Answer 1

Answer:

sorry I don't anderstand your questions

Answer 2

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