**Translating Sentences into Symbolic Form :**

Have you ever written a sentence in short hand or used acronyms to represent words ?

In math we do that as well. In this topic, you will learn how to translate a sentence into symbolic form.

You will also learn how to change the meaning of a sentence, by using a symbol

We can use the following stuff to translate sentences into symbolic form.

**∼** = Not

∧ = And (Conjunction)

∨ = Or (Dis junction)

--> = If....then

<--> = If and only if

**Example 1 : **

Translate the following sentence into symbolic form :

The earth is a planet

**Translation : **

E

**Example 2 : **

Translate the following sentence into symbolic form :

David is not a soccer player

**Translation : **

**∼** S

**Example 3 : **

Translate the following sentence into symbolic form :

John is intelligent and handsome

**Translation : **

I ∧ H

**Example 4 : **

Translate the following sentence into symbolic form :

He watches TV but not sports programs

**Translation : **

Note :** But** is the same as **And**

So, we have

T ∧ **∼** S

**Example 5 : **

Translate the following sentence into symbolic form :

I have neither the time nor the money to do the project

**Translation : **

Note : Neither A nor B is the same as not A and not B

So, we have

**∼ T** ∧ **∼** M

**Example 6 : **

Translate the following sentence into symbolic form :

It is false that Michael is running for President and Donald Trump is endorsing him.

**Translation : **

**∼** (M ∧ D)

**Example 7 : **

Translate the following sentence into symbolic form :

If the label does not read "POISON" then I can drink it

**Translation : **

**∼** P --> D

**Example 8 : **

Translate the following sentence into symbolic form :

The cow is brown if and only if the milk is chocolate

**Translation : **

B <--> C

**Example 9 : **

Translate the following sentence into symbolic form :

Take rest or play games

**Translation : **

T ∨ P

**Example 10 : **

Translate the following sentence into symbolic form :

Read the book, and take a test or do a project

**Translation : **

(R ∧ T) ∨ P

**Example 11 : **

Translate the following sentence into symbolic form :

Read the book and take a test, or do a project

**Translation : **

R ∧ (T ∨ P)

**Example 12 : **

Translate the following sentence into symbolic form :

Read the book and don't take the test, or do a project

**Translation : **

(R ∧ **∼ T**) ∨ P

**Example 13 : **

Translate the following sentence into symbolic form :

Write the dis junction of D and S.

**Translation : **

D ∨ S

**Example 14 : **

Translate the following sentence into symbolic form :

Write the negation of **∼** W

**Translation : **

W

**Example 15 : **

Translate the following sentence into symbolic form :

Write the conjunction of A and **∼** F

**Translation : **

A ∧ **∼** F

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