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

Translating Sentences into Symbolic Form - Examples

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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