Using the letter indicated for the component statements tran

Using the letter indicated for the component statements, translate the following compound statements into symbolic notation.

a. A: the tractor wins; B: the truck wins; C: the race will be exciting

Whether the tractor wins or the truck wins, the race will be exciting.

b. A: snow; B: rain; C: yesterday was cloudy

Yesterday was cloudy but there was neither snow nor rain.

c. A: Koalas will be saved; B: climate change is addressed; C: rising water levels

Koalas will be saved only if climate change is addressed; furthermore, failure to address climate change will cause rising water levels.

d. A: the city\'s economy will improve; B: a strong school system

The city\'s economy will improve conditional upon a strong school system.

e. A: the city\'s economy will improve; B:a strong school system

A strong school system is a necessary condition for the city\'s economy to improve.

Solution

Answer:

1)

Consider the given compound statement : \" Whether the tractor wins or the truck wins, the race will be exciting\"

let us denote :

A: the tractor wins;    B: the truck wins;      C: the race will be exciting

Then the above compound statement can be written in symbolic form as follows :

( A V B ) C

2) Consider the given compound statement : \"Yesterday was cloudy but there was neither snow nor rain\"

let us denote :

A: snow;      B: rain;         C: yesterday was cloudy

Then the above compound statement can be written in symbolic form as follows :

C [ ¬ A V ¬ B ]

3) Consider the given compound statement : \"Koalas will be saved only if climate change is addressed; furthermore, failure to address climate change will cause rising water levels\" .

let us denote :

A: Koalas will be saved;         B: climate change is addressed;        C: rising water levels

Then the above compound statement can be written in symbolic form as follows :

( B A ) ( ¬ B C )

4) Consider the given compound statement : \"The city\'s economy will improve conditional upon a strong school system\".

let us denote :

A: the city\'s economy will improve; B: a strong school system

Then the above compound statement can be written in symbolic form as follows :

A B.

5). Consider the given compound statement : \"A strong school system is a necessary condition for the city\'s economy to improve \".

let us denote :

A: the city\'s economy will improve; B:a strong school system

B A