# Math

posted by .

Find the number of elements in A1∪A2∪A3, supposing that there are
103 elements in A1,
992 elements in A2,
10011 elements in A3,
in each of the following situations:

(a) The sets are pairwise disjoint, that is, no pair has common elements, that is, the intersection of the two sets in any given pair is empty.

(b) A1⊆A2⊆A3.

(c) Each pairwise intersection of these sets has the same cardinality 16 , and the intersection of all three sets has cardinality 2.

• Math -

b) They are all in A3 so 10011

c) draw a Venn diagram
Only in A1 = 103 - 44 = 59
Only in A2 = 992- 44= 948
Only in A3 = 10011 - 44 = 9967
shared = 3*14 + 2 = 44
sum = 11018

• Math C redone -

should subtract 30 (14*2+2), not 44
c) draw a Venn diagram
Only in A1 = 103 - 30 = 73
Only in A2 = 992- 30= 962
Only in A3 = 10011 - 30 = 9981
shared = 3*14 + 2 = 44
sum = 11060

• Math -

Thanks man!

• Math -

You are welcome :)

## Similar Questions

1. ### math

For the set X={m,n.p,q,r,s}, let R be the relation on P(X) (power set) given by A R B iff A and B have the same number of elements. List all the elements in {m}/R (equivalence class); in {m,n,p,q,r,s}/R. How many elements are in X/R?
2. ### math

If there are 6 elements in (A U B) and 1 Element in (A N B) answer the following: A. What is the maximum number of elements possible for A?
3. ### Math

If there are 6 elements in ( A u B ) and 1 element in ( A n B ) answer the following A. What is the maximum number of elements possible for A?
4. ### mathematics

The numbers 1,2,…,17 are divided into 5 disjoint sets. One set has 5 elements, one set has 4 elements, two sets have 3 elements and the last set contains the 2 remaining elements. Two players each choose a number from 1 to 17 at …
5. ### maths

The numbers 1,2,…,17 are divided into 5 disjoint sets. One set has 5 elements, one set has 4 elements, two sets have 3 elements and the last set contains the 2 remaining elements. Two players each choose a number from 1 to 17 at …
6. ### probability

PROBLEM 2: SET OPERATIONS AND PROBABILITIES (3 points possible) Find the value of P(A∪(Bc∪Cc)c) for each of the following cases: The events A, B, C are disjoint events and P(A)=2/5. P(A∪(Bc∪Cc)c)= incorrect …
7. ### Math - sets

Suppose A, B, and C are sets. In at least one of the following situations, one can conclude that A = B. Identify those cases where this conclusion does apply. (i) A ∪ C = B ∪ C A={1,2},A={1,2}, B={2,3}B={2,3} and C={1,2,3}.C={1,2,3}. …
8. ### Sets

Suppose Set B contains 69 elements and the total number elements in either Set A or Set B is 107. If the Sets A and B have 13 elements in common, how many elements are contained in set A?
9. ### Algebra

Suppose Set B contains 69 elements and the total number elements in either Set A or Set B is 107. If the Sets A and B have 13 elements in common, how many elements are contained in set A?
10. ### Sets

Suppose Set B contains 69 elements and the total number elements in either Set A or Set B is 107. If the Sets A and B have 13 elements in common, how many elements are contained in set A?

More Similar Questions