4_Section_Answers (1)-1
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Apr 3, 2024
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Section #4 Exercises
Symbolize each proposition.
1. No Airlines charge fares that are affordable.
~A
2. Planting trees is one effective way of offsetting carbon dioxide emissions. P
3. NASA has discovered an act of sabotage, but the damage is minor.
N&D
4. Japan is not in North America and Canada is not in Asia.
~J&~C
5. Some doctors encourage people to take 1,000 mg of vitamin C daily to ward off colds.
C
6. There is no way that there is both an overall slump in the housing market and you are doing just fine
financially.
~(S&F) *you can also symbolize this as ~Sv~F Find the Truth Function (i.e., Truth Tables) for each.
7. Mendoza will either not have ramen or not have soup for lunch.
~R
v~S
R
S
~
R
v
~
S
T
T
F
T
F
F
T
T
F
F
T
T
T
F
F
T
T
F
T
F
T
F
F
T
F
T
T
F
8. Mendoza will have neither ramen nor soup for lunch.
~(RvS)
R
S
~
(R
v
S)
T
T
F
T
T
T
T
F
F
T
T
F
F
T
F
F
T
T
F
F
T
F
F
F
Are the following Tautologies, Taut-falsities or Contingent?
9. Mendoza will either have ramen for lunch or not, unless he will not have ramen for lunch.
(Rv~R)
v~R
R
(R
v
~
R)
v
~
R
T
T
T
F
T
T
F
T
F
F
T
T
F
T
T
F
*This sentence is a Tautology
because its truth function is true on every row.
10. Mendoza will and will not have soup for lunch, but he will have soup for lunch.
(S&~S)
&S
S
(S
&
~
S)
&
S
T
T
F
F
T
F
T
F
F
F
T
F
F
F
*This sentence is a Taut-falsity
because its truth function is false on every row.
11. Mendoza will and will not have curry for lunch, or he will not have curry for lunch.
(C&~C)v~C
C
(C
&
~
C)
v
~
C
T
T
F
F
T
F
F
T
F
F
F
T
F
T
T
F
*This sentence is a Contingent because its truth function is true on at least one row and false on at least one row. 12. It is not the case that, Mendoza will not have ramen and not have curry for lunch, unless he will have neither ramen nor curry for lunch.
~(~R&~C)
v~(RvC)
R
C
~
(~
R
&
~
C)
v
~
(R
v
C)
T
T
T
F
T
F
F
T
T
F
T
T
T
T
F
T
F
T
F
T
F
T
F
T
T
F
F
T
T
T
F
F
F
T
T
F
F
T
T
F
F
F
T
F
T
T
F
T
T
F
F
F
*This sentence is a Tautology
because its truth function is true on every row.
Using Truth Tables, are these sentences equivalent, contradictory, or consistent? Use the truth-table method to determine whether the following two sentences are equivalent.
13. R
vS S
vR
R
S
R
v
S
S
v
R
T
T
T
T
T
T
T
T
T
F
T
T
F
F
T
T
F
T
F
T
T
T
T
F
F
F
F
F
F
F
F
F
*This pair of sentences is equivalent
because they have the same truth function (i.e., the same value in
both their main connective columns).
14. ~S
v~R ~(S&R) R
S
∼
S
v
~ R
~
(S
&
R) T
T
F
T
F
F
T
F
T
T
T
T
F
T
F
T
F
T
T
F
F
T
F
T
F
T
T
T
F
T
T
F
F
F
F
T
F
T
T
F
T
F
F
F
*This pair of sentences is equivalent
because they have the same truth function (i.e., the same value in
both their main connective columns).
15. ~S
vR S
&
∼
R R
S
~
S
v
R
S
&
∼
R
T
T
F
T
T
T
T
F
F
T
T
F
T
F
T
T
F
F
F
T
F
T
F
T
F
F
T
T
T
F
F
F
T
F
T
F
F
F
T
F
* This pair of sentences is NOT
equivalent
because they do not have the same truth function (i.e., the same value in both their main connective columns). In fact, this pair of sentences happens to be contradictory because they have the exact opposite truth function (i.e., the opposite values in both their main connective columns).
16. ~(SvR) ~S&~R R
S
~
(S
v
R)
~
S
&
~
R
T
T
F
T
T
T
F
T
F
F
T
T
F
F
F
T
T
T
F
F
F
T
F
T
F
T
T
F
F
T
F
T
F
F
F
T
F
F
F
T
F
T
T
F
*This pair of sentences is equivalent
because they have the same truth function (i.e., the same value in
both their main connective columns).
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