Problem Set 1: PHIL 1068 Elementary Logic: Due 4 ... - Philosophy
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Problem Set 1: PHIL 1068 Elementary Logic: Due 4:00PM 28 January 2011 Student ID Number
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1. (15 marks) True or false? Circle ‘T’ if the statement is true. Circle ‘F’ if the statement is false. For this question, you should assume that ϕ is a WFF of SL. T T T T T T T T T T T T T T T
F F F F F F F F F F F F F F F
“Be careful Yoda!” is a statement. The conclusion of a valid argument must be true. If an argument is not sound, then that argument is not valid. Some sound arguments have false conclusions. “∼” is the main connective of “∼ ∼ (D ↔ ∼A)”. Whenever “(A&B)” is true, “(D ∨ A)” is also true. If ϕ contains the symbol “)” then ϕ contains a two-place connective. Logic describes how people reason. Some WFF of SL contains exactly 46 symbols. The word “drawer” is lexically ambiguous. ϕ might not be an expression of SL. ϕ is either a disjunction or a conjunction. The scope of “&” in “(∼(∼P &Q) → P )” is “(∼P &Q)”. Every SL WFF contains at least one connective. The antecedent of “(∼P → Q)” is “P ”. /15
2. (10 marks) Which of the following is a valid argument? Circle “Yes” if it is a valid argument. Circle “No” if it is not a valid argument. Yes No Some birds cannot fly. So, not all birds can both fly and swim. Yes
No
He wants to be rich. Every rich person is unhappy. So, he wants to be unhappy.
Yes
No
English is not widely spoken in Jakarta. English is widely spoken in Jakarta. Therefore, English is widely spoken.
Yes
No
If Plato knew Picasso then Socrates never smiled. Socrates never smiled. Therefore, either Plato knew Picasso or Plato.
Yes
No
If red is a color, then red is a color. /10 1
3. (4 marks) Which of the following five expressions is not a WFF of SL? (A → B) (((A ↔ A) ↔ ((∼B ∨ A) ∨ ∼(B ← D))) ∼ ∼ (((D ↔ A)&A) ((A&B)& ∼ A) ∼(∼B) /4 4. (16 marks) Fill in the blanks with an SL WFF to make correct truth tables. Each WFF must contain exactly three two-place connectives.
a.
Q
R
P
T T T T F F F F
T T F F T T F F
T F T F T F T F
c.
P
Q
T T F F
T F T F
F T F F F T T T
b.
P
Q R
T T T T F F F F
T T F F T T F F
T F T F T F T F
T F T F T T T T
B
F F F T
d.
T F
F T
/16 5. (15 marks) Make a correct truth table for each of the following WFFs of SL. a. ((A&B) ↔ A3 )
