Assignment 2
Deadline Wednesday, June7 at 9 PM.
Submit to: kamillasmith27@gmail.com Your task is to translate English sentences into the language of logic according to the
pattern explained below.
Suppose you have to translate the sentence: It is raining today. This sentence can be symbolized simply as: R But if I want to say: It is raining today and I will stay home. This sentence will be symbolized as: R&S
Here R stands for “It is raining today,” while S stands for “I will stay home.”
For the word “and” we will use the symbol &.
Please note that you can use any letters of the alphabet to symbolize a given
statement. Now write the symbolic translations next to each sentence (the first two are
examples already solved):
1. Today is Monday. M 2. Anna saw a movie and she called her father. S&C *(Note again that you can choose any letters to symbolize this sentence. For example
M & F. What matters is that you recognize that the sentence is a “conjunction,”
meaning it conjoins two “atomic propositions,” the proposition S (Anna saw a
movie) and the proposition C (She called her father.)
Now your turn:
3. Max works full-time.
4. Max is a senior in college and he works full-time.
5. John is a sophomore.
6. John plays basketball and John likes movies.
7. Joanna plays piano and she is a junior.
8. John will graduate in two years and he will work full-time.
9. Max likes movies and he plays the piano.
10. They got married and they had a baby.
11. They had a baby and they got married. Now, suppose you translated the sentence “Felix went to work” as W.
But if I say “Felix did not go to work,” you will have to negate the sentence in the
following way:
–W
We will use the “minus” symbol express negations.
Negate the following sentences (the first two are examples): 12. It is raining today. – R
13. Today is Monday. –M 14. John went to work.
15. John went to school.
16. Nancy went to the movies and she did her homework.
17. Anna went straight home.
18. It is raining today. Now be careful. How would you negate the sentence “It is not raining today”?
This depends on you. If you symbolize the sentence “It is raining today” as R,
T\hen the sentence “It is not raining today” would be – R. In this case, negating “It
is not raining today” would look like:
– –R This double negation will amount to R.
So, continue negating:
19. Anna is at school.
20. Anna is not at school. We already learned that a sentence, such as “Anna saw a film and she went to a
museum” can be translated into symbolic logic as:
F&M
Suppose now you want to translate the sentence:
“Anna saw a film or she went to the museum.” Here you cannot use the symbol &. For the word “or” we will use v.
So, the sentence will look like:
FvM
Continue translating:
21. Ann is at work or she went to school.
22. John is a fool or he is unaware of the danger.
\23. Today is Monday or it is Tuesday.
24. Today is either Wednesday or Thursday.
25. I will go to Paris or to London.
26. I will stay home or I will go to a restaurant.
27. I will go home or I will not go home.
28. It is Friday or it is not Friday.
29. I will do my homework or I will not get a good grade.
30. I will have coffee or I will be sleepy. The above sentences are examples of three different kinds of statements:
Conjunctions
Negations
Disjunctions Each type of sentence is symbolized differently:
& (stands for conjunctions)
– (stands for negations)
v (stands for disjunctions) Now go back to all the sentences and find all conjunctions and disjunctions (write in
parenthesis “conjunction” next to a conjunction, and “disjunction” next to a
disjunction).
Be careful! A sentence of this kind: “Today is Monday and it is not raining,” is
primarily a conjunction even though there is a negation in the second part of the
sentence. So, there is a negation but the sentence is first and foremost a
conjunction. This means it would be incorrect to say that the sentence is a negation.

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