Math 110- 5.1 Sets and Venn Diagrams

What do you do when you see “n”

Ex: A n B

A = {5,6,7,8,9,10,11,12}

B = {8,10,12,14,16,18}

Keep what is in common between both sets

Answer: A n B = {8,10,12}

What do you do when you see “u”

Ex: A u B

A = {5,6,7,8,9,10,11,12,13}

B = {9,11,13,15,17,19}

List all the numbers in both sets (do not repeat numbers though)

Answer: {5,6,7,8,9,10,11,13,15,17,19}

What is an intersection? How is it written?

The set consisting of all those elements that belong to both A and B

Written as “n”

What is a union? How is it written?

The set consisting of all those elements that belong to both A or B or both

Written as “u”

What do you do when you see ‘ written after a letter?

Ex: S’

U = {1,2,3,4,5,6,7}

S = {1,2,3,4}

Get rid of the numbers both sets have in common

Answer: S’ = {5,6,7}

On a Venn diagram what part is shaded in for a union?

The whole Venn diagram is shaded (even the part in the middle)

On a Venn diagram what part is shaded in for an intersection?

Just the middle part between the two circles

What is the inclusion-exclusion principle formula?

n(S u T) = n(s) + n (T) - n( S n T)

If it is a union “u” what do you shade in for a Venn Diagram?

Shade in everything

If it is a intersection “n” what do you shade in for a Venn Diagram?

Just the part that overlaps

If it is a compliment ‘ what do you shade in for a Venn Diagram?

Everything except for the letter that is being complimented

Ex: S’ n T’

Shade everything outside but not S or T

Ex: T’

Shade S side and outside but not T side

Simplify S’ U (S n T)’

S’ U T’

Simplify (S’ U T)’

S n T’

Simplify T U (S n T)’

T u S’ u T’

= U (universal set)