**Venn Diagram Reasoning Tricks :**

Venn diagram reasoning is a way of picturing relationships between different groups of things.

Venn Diagram Reasoning can be understood easily in the following three scenarios.

**Scenario 1 : **

All of the members of A are also members of B. Some of the members of B are also members of A.

This situation can be expressed using Venn diagram as given below.

**Scenario 2 : **

Some of the members of A are also members of B and vice versa.

This situation can be expressed using Venn diagram as given below.

**Scenario 3 : **

No members of A are members of B and vice versa.

This situation can be expressed using Venn diagram as given below.

**Universe : **

A rectangle. The universe is not "everything", but "everything" you are dealing with right now.

**Example :**

Some angles are right angles and some angles are obtuse angles.

Here, we are dealing with angles. So the universe is angles.

This situation can be expressed using Venn diagram as given below.

**Example 1 : **

Express the following situation using Venn diagram :

Jack likes cake and ice cream. Betty likes brownies, both of them like cookies and neither like pie.

**Answer : **

**Example 2 : **

Express the following situation using Venn diagram :

John plays football and baseball. Daniel plays basketball. They both play soccer and neither plays hockey.

**Answer : **

**Example 3 : **

Express the following situation using Venn diagram :

All pigs eat corn

**Answer : **

**Example 4 : **

Express the following situation using Venn diagram :

Some apples are green

**Answer : **

**Example 5 : **

This Venn diagram given below illustrates the number of pizzas sold yesterday at Polo Verde Pizzeria categorized by toppings.

Use this information to answer the following questions.

(i) How many pizzas had pepperoni ?

(ii) How many pizzas had sausage and olives ?

(iii) How many pizzas were sold altogether ?

(iv) How many pizzas had sausage ?

(v) How many pizzas had all three toppings ?

**Answers : **

**Answer (i) : **

Number of pizzas had pepperoni :

= 20 + 40 + 4 + 2

= 66

**Answer (ii) : **

Number of pizzas had sausage and olives :

= 4 + 16

= 20

**Answer (iii) : **

Number of pizzas were sold altogether :

= 20 + 11 + 7 + 2 + 16 + 40 + 4

= 100

**Answer (iv) : **

Number of pizzas had sausage :

= 11 + 16 + 4 + 2

= 33

**Answer (v) : **

Number of pizzas had all three toppings :

= 4

After having gone through the stuff above, we hope that the students would have understood Venn diagram reasoning.

Apart from the stuff given on "Venn diagram reasoning tricks", if you need any other stuff, please use our google custom search here.

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