TRANSLATING SENTENCES INTO SYMBOLIC FORM

Translating Sentences into Symbolic Form - Examples

Translate the following sentence into symbolic form : 

Example 1 : 

The earth is a planet

Solution :

Let E be the earth.

Translation : 

E

Example 2 : 

David is not a soccer player

Solution :

Let S be the soccer player.

Translation : 

∼ S

Example 3 : 

John is intelligent and handsome

Solution :

Let J represents his name John and H be handsome.

Translation : 

I ∧ H

Example 4 : 

He watches TV but not sports programs

Solution :

T be television and S be sports.

Translation : 

Note : But is the same as And

So, we have

T ∧ ∼ S

Example 5 : 

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

Solution :

T be time and M be money.

Translation : 

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

So, we have

∼ T ∧ ∼ M

Example 6 : 

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

Solution :

Let M be Michael and D be Donald Trump.

Translation : 

∼ (M ∧ D)

Example 7 : 

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

Solution :

Let M be Michael and D be Donald Trump.

Translation : 

∼ P --> D

Example 8 : 

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

Solution :

Translation : 

B <--> C

Example 9 : 

Take rest or play games

Solution :

Translation : 

T ∨ P

Example 10 : 

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

Solution :

Translation : 

(R ∧ T) ∨ P

Example 11 : 

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

Solution :

Translation : 

R ∧ (T ∨ P)

Example 12 : 

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

Solution :

Translation : 

(R ∧ ∼ T) ∨ P

Example 13 : 

Write the dis junction of D and S.

Solution :

Translation : 

D ∨ S

Example 14 : 

Write the negation of ∼ W

Solution :

Translation : 

W

Example 15 : 

Write the conjunction of A and ∼ F

Solution :

Translation : 

A ∧ ∼ F

Example 16 : 

Turkey is a member of NATO but Iraq is not.

Solution :

T= Turkey is a member of NATO.

I = Iraq is a member of NATO.

Translation : 

T & ~I

Example 17 : 

 Either Brazil or Argentina Destroys its rain forests.

Solution :

B =Brazil destroys its rain forests.

A = Argentina destroys its rain forests.

Translation : 

A v B

Example 18 :

High definition TV is a technological marvel, but it is expensive.

Solution :

H = High definition TV is a technological marvel.

E = High definition TV is expensive.

Translation : 

H & E

Example 19 :

If Scotland declares independence, then England reduces imports.

Solution :

S= Scotland declares independence.

E = England reduces imports.

Translation : 

S -> E

Example 20 :

Scotland declares independence only if England reduces imports.

Solution :

S= Scotland declares independence.

E = England reduces imports.

Translation : 

S -> E

Example 21 :

Scotland declares independence if England reduces imports.

Solution :

• S = Scotland declares independence.
• E = England reduces imports.

E -> S

Example 22 :

China does not export nuclear energy unless Russia does.

Solution :

• C = China exports nuclear energy.
• R = Russia exports nuclear energy.

~C v R

C -> R

~R -> ~C

Example 23 :

Ozone depletion in the atmosphere is a sufficient condition for increased cancer rates.

Solution :

• O = The ozone in the atmosphere is depleted.
• C = Cancer rates increase.

O -> C

Example 24 :

Either Hungary adopts political reforms and Romania freezes wages or Bulgaria broadens services.

Solution :

• H = Hungary adopts political reforms.
• R = Romania freezes wages.
• B = Bulgaria broadens services.

(H & R) v B

Example 25 :

Either Sweden or Norway reduce deficit spending.

Solution :

• S= Sweden reduces deficit spending.
• N = Norway reduces deficit spending.

S v N

Example 26 :

Neither Sweden nor Norway reduce deficit spending.

Solution :

• S= Sweden reduces deficit spending.
• N = Norway reduces deficit spending.

~(S v N)

~S & ~N

Example 27 :

Peru increases military spending unless both Guyana and Bolivia do not improve health care.

Solution :

• P = Peru increases military spending.
• G = Guyana improves health care
• B = Bolivia improves health care

P v (~G & ~B)

~(~G & ~B) -> P

(G v B) -> P

Example 28 :

Lydia abandons terrorism if and only if neither Egypt nor Saudi Arabia closes its embassy.

Solution :

• L = Lydia abandons terrorism.
• E = Egypt closes its embassy.
• S = Saudi Arabia closes its embassy.

L <-> ~(E v S)

L <-> (~E & ~S)

Example 29 :

If either Uganda or Rwanda receives increased aid, then neither Kenya nor Burundi protects its endangered species.

Solution :

• U = Uganda receives increased aid
• R = Rwanda receives increased aid
• K = Kenya protects its endangered species
• B = Burundi protects its endangered species

(U v R) -> ~(K v B)

(U v R) -> (~K & ~B)

Example 30 :

Argentina exports beef, and Brazil exports coffee or Chile exports wood products.

Solution :

• A = Argentina exports beef.
• B = Brazil exports coffee.
• C = Chile exports wood products.

A & (B v C)

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