The order of evaluation is not important.

A ∩ B = B ∩ A

Parentheses need to be evaluated first.

A ∪ (B ∩ C ) = (A ∪ B) ∩ (A ∪ C)

A ∩ (B ∪ C ) = (A ∩ B) ∪ (A ∩ C)

Let's start with an example to contrast the difference between union and intersection, then move on to examples with combined operations.

In a factory that consists of 120 skilled workers, 59 possess a diploma, 66 possess a degree, 20 possess neither a diploma nor a degree. Find

(a) the number of workers who possess both a diploma and a degree.

(b) the number of workers who possess a diploma or a degree.

Let U = {skilled workers in the factory}

Let D = {workers who possess a diploma}

Let I = {workers who possess a degree}

(a) n(D ∩ I) = x

Hence, the number of workers who possess both a diploma and a degree is 25 persons.

(b)

Hence, the number of workers who possess a diploma or a degree is 100 persons.

The Venn diagram shows the relationship between three sets A, B, and C with the universal set, U. List the elements of

(a) (A ∩ B) ∪ C,

(b) A ∩ (B ∪ C),

(c) (A ∪ B) ∩ C,

(d) A ∪ (B ∩ C).

(a)

(A ∩ B) = {3, 5}

(A ∩ B) ∪ C = {3, 4, 5, 6, 9, 10}

(b)

(B ∪ C) = {3, 4, 5, 6, 7, 8, 9, 10}

A ∩ (B ∪ C) = {3, 4, 5}

(c)

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7, 8}

(A ∪ B) ∩ C = {4, 5, 6}

(d)

(B ∩ C) = {5, 6}

A ∪ (B ∩ C) = {1, 2, 3, 4, 5, 6}

Based on the Venn diagram in Example 2, list the elements of

(a) A' ∩ (B ∪ C),

(b) (A' ∪ C') ∩ B.

(a)

(B ∪ C) = {3, 4, 5, 6, 7, 8, 9, 10}

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

A' ∩ (B ∪ C) = {6, 7, 8, 9, 10}

(b)

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

C' = {1, 2, 3, 7, 8, 11, 12}

(A' ∪ C') = {1, 2, 3, 6, 7, 8, 9, 10, 11, 12}

(A' ∪ C') ∩ B = {3, 6, 7, 8}

The Venn diagram shows the universal set U and sets A, B, and C. On a separate Venn diagram, shade the region for

(a) (A ∪ B) ∩ C',

(b) (B ∩ C) ∪ (A ∪ B)',

(a)

(A ∪ B)

(A ∪ B) ∩ C'

(b)

(B ∩ C)

(B ∩ C) ∪ (A ∪ B)

In the Venn diagram, A, B, and C are three sets whereas U is the universal set. The number of elements in a few subsets are shown and n(U) = 40. Find

(a) n(B)

(b) n[(A ∩ B) ∪ C],

(c) n[A' ∪ (B ∩ C')].

(a)

Create an equation from the information given by the Venn diagram.

(b)

n[(A ∩ B) ∪ C] = 8 + 14 = 22

(c)

n[A' ∪ (B ∩ C')] = 8 + 5 + 14 + 3 = 30

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**proof for aU(b^c)=(aUb)^(aUc)** Not rated yet

i want proof for that
by ven daigram
Damien: Perhaps you could post a photo of what you've tried, and we can work on your solution.

**Combined Operations** Not rated yet

I need for the combined to be explained in a simple term.
Damien: Noted. I'll get to it in due time.