Are you finding it hard to understand and solve Sets with Venn diagram in your JAMB and WAEC mathematics questions?

In this lesson…

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

##### ALSO SEE: How To Identity And Interpret Basic Set Symbols

*Take note.*

A link for you to practice real past 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.

*Take note.*

(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)*

THE EQUATION:

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

**Addition**

: 57 – x + 7 = 50

**Collect like terms**

: 57 – 50 + 7 = x

**Addition before subtraction**

: 57 – 43 = x

14 = x

FINAL ANSWER:

Number of students who both read a book and watch television (B \cap T) represented as (x)

=

14

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