# How To Solve Sets With Venn Diagram

Are you finding it difficult to understand and solve Sets with Venn diagram?

In this lesson,

You will learn the step-by-step method for solving questions on Sets with Venn diagrams in your mathematics exam.

#### ALSO SEE: How To Identify and Interpret Basic Set Symbols

Take note.

A link for you to practice past exam questions on sets with Venn diagrams is included at the bottom of this lesson.

## Solving sets with Venn diagram

Let’s take an example.

QUESTION:

50 students were asked what they did last night. 16 said they read a book, and 41 said they watched television. If 7 said they did neither, how many did both?

### 1. List the details in the question

• Total number of students is the Universal Set (\mho) = 50
• Number of students who read a book is subset (B) = 16
• Number of students who watch Television is subset (T) = 41
• Number of students who neither read a book (B’) nor watch Television (T’) is therefore, B’ \cup T’ or (B \cup T)’ = 7
• Number of students who both read a book and watch television (B \cap T) = ?? Let’s represent the unknown with (x)

### 2. Transfer the details into a Venn diagram.

NOTE THAT

(x) is being subtracted from the subset B and T because what they both have in common (x) must be removed to get what they each have alone.

### 3. Convert your Venn diagram to an equation.

Add all the elements in your Venn diagram and equate them to the Universal Set.

In other words,

(Subset B) + (Intersection) + (Subset T) + (Complement) = (Universal Set)

• 16 – x + x + 41 – x + 7 = 50

### 4. Solve for x in the equation

16 – x + x + 41 – x + 7 = 50

• (-x) cancels (+x)

: 16 + 41 – x + 7 = 50

: 57 – x + 7 = 50

• Collect like terms

: 57 – 50 + 7 = x

: 57 – 43 = x

14 = x