18
Formal Logic
c. Either the food is good and the service is excellent, or else the price is high.
d. Neither the food is good nor the service excellent.
e. If the price is high, then the food is good and the service is excellent.
12. Write the negation of each statement.
a. The processor is fast but the printer is slow.
b. The processor is fast or else the printer is slow.
c. If the processor is fast, then the printer is slow.
d. Either the processor is fast and the printer is slow, or else the file is damaged.
e. If the file is not damaged and the processor is fast, then the printer is slow.
f. The printer is slow only if the file is damaged.
13. Using the letters indicated for the component statements, translate the following compound statements
into symbolic notation.
a. A: prices go up; B: housing will be plentiful; C: housing will be expensive
If prices go up, then housing will be plentiful and expensive; but if housing is not expensive, then it will
still be plentiful.
b. A: going to bed; B: going swimming; C: changing clothes
Either going to bed or going swimming is a sufficient condition for changing clothes; however, changing clothes does not mean going swimming.
c. A: it will rain; B: it will snow
Either it will rain or it will snow but not both.
d. A: Janet wins; B: Janet loses; C: Janet will be tired
If Janet wins or if she loses, she will be tired.
e. A: Janet wins; B: Janet loses; C: Janet will be tired
Either Janet will win or, if she loses, she will be tired.
14. Using the letters 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.
15. Let A, B, and C be the following statements:
A Roses are red.
B Violets are blue.
C Sugar is sweet.
Translate the following compound statements into symbolic notation.
a. Roses are red and violets are blue.
b. Roses are red, and either violets are blue or sugar is sweet.
Formal Logic
c. Either the food is good and the service is excellent, or else the price is high.
d. Neither the food is good nor the service excellent.
e. If the price is high, then the food is good and the service is excellent.
12. Write the negation of each statement.
a. The processor is fast but the printer is slow.
b. The processor is fast or else the printer is slow.
c. If the processor is fast, then the printer is slow.
d. Either the processor is fast and the printer is slow, or else the file is damaged.
e. If the file is not damaged and the processor is fast, then the printer is slow.
f. The printer is slow only if the file is damaged.
13. Using the letters indicated for the component statements, translate the following compound statements
into symbolic notation.
a. A: prices go up; B: housing will be plentiful; C: housing will be expensive
If prices go up, then housing will be plentiful and expensive; but if housing is not expensive, then it will
still be plentiful.
b. A: going to bed; B: going swimming; C: changing clothes
Either going to bed or going swimming is a sufficient condition for changing clothes; however, changing clothes does not mean going swimming.
c. A: it will rain; B: it will snow
Either it will rain or it will snow but not both.
d. A: Janet wins; B: Janet loses; C: Janet will be tired
If Janet wins or if she loses, she will be tired.
e. A: Janet wins; B: Janet loses; C: Janet will be tired
Either Janet will win or, if she loses, she will be tired.
14. Using the letters 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.
15. Let A, B, and C be the following statements:
A Roses are red.
B Violets are blue.
C Sugar is sweet.
Translate the following compound statements into symbolic notation.
a. Roses are red and violets are blue.
b. Roses are red, and either violets are blue or sugar is sweet.