Question

4. Let the universal set be E= {natural numbers less than 26). and letA = {Squares less than 26)B = (Odd Numbers less than 26)C = {Even Squares less than 26)Part A: Complete the Venn diagram with the number of elements in each section.Part B: Determine the elements in (ANB).Part C. Determine the elements in -AU BUC).Part D: Determine the elements in (AN-BNC)

Answer 1

First, it will be useful to write explicitly the elements of each set:

E = {1,2,3, ... ,25}

A = {1,4,9,16,25}

B = {1,3,5,7,9,11,13,15,17,19,21,23,25}

C = {4,16}

Part A

# of elements of E = 25

# of elements of A = 5

# of elements of B = 13

# of elements of C = 2

A ∩ B = {1,9,25} # (A ∩ B) = 3

A ∩ C = {4,16} # (A ∩ C) = 2

B ∩ C = {} # (B ∩ C) = 0

A ∩ B ∩ C = {} # (A ∩ B ∩ C ) = 0

The inserctions of the different circles are the intersections of the differents sets.

We used the #'s computed above to fill the different zones of the diagram.

Part B

It is already done above.

A ∩ B = {1,9,25}

Part C

Meaning of ~ symbol: ~ A = bar over A = complement of the set A = E - A = elements in E that are not in A

E = {1,2,3, ... ,25}

A = {1,4,9,16,25}

B = {1,3,5,7,9,11,13,15,17,19,21,23,25}

C = {4,16}

A U B U C = {1,3,4,5,7,9,11,13,15,16,17,19,21,23,25}

So the complement of the set: A U B U C , is the set that contains the elements in E (the universal set) that are not in A. So:

~ A U B U C = {2,6,8,10,12,14,18,20,22,24}

Part D

(~ B) = elements of E that are not in B

A U (~ B) U C =