课程名称︰基本逻辑
课程性质︰系必修
课程教师︰邓敦民
开课学院：文学院
开课系所︰哲学系
考试日期（年月日）︰2015/4/16
考试时限（分钟）：170 min
试题 :
1. Which of the following are true and which are false?
(Note: just write down "True" or "False". No explanation)
(a)(2%) If all the premises of an argument are true and the conclusion is false,
then the argument is invalid.
(b)(2%) Every argument whose conclusion is logically equivalent to one of its
premises is valid.
(c)(2%) P is truth-functionally true if and only if {P} is truth-functionally
consistent.
(d)(2%) If P and Q are truth-functionally equivalent, then a completed
truth-tree for {P≡Q} will be open.
(e)(2%) If a set of sentence of SL is truth-functionally inconsistent, then
there is a sentence P such that both P and ~P are derivable from the
set in SD(i.e., the natural deduction system for SL).
2.(12%) Symbolise the following argument by using these abbreviations:
M: The maid committed the murder.
B: The bulter committed the murder.
C: The cook committed the murder.
K: The murder weapon was a knife.
"Either the maid or the bulter committed the murder unless the cook did it.
The cook did it only if a knife was the murder weapon;
moreover, if a knife was the murder weapon,
neither the bulter nor the maid did it. Therefore the cook did it."
3. For each of the following sentences, specify its main connective and the
immediate sentential components.
(a)(4%) ~((A≡A)≡(~A≡A))
(b)(4%) (Av((Av~A)vA))
4. Prove the following by constructing appropriate truth-tables:
(a)(5%) ((A⊃B)⊃A)⊃A is truth-functionally true.
(b)(5%) ~C≡D and ~(C≡D) are truth-functionally equivalent.
5. Prove the following by the truth-tree mrthod:
(a)(5%) {A⊃B,B⊃A}╞ A≡B
(b)(5%) {H＆(~K⊃M),~(H⊃M)}╞ K
6.(10%) Determine whether the following claim is true. If it is true, prove it
either by constructing an appropriate truth-table or by using the
truth-tree method. If it is not true, specify a truth-value assignment
to show this.
{((A≡B)≡A)≡A}╞ B
7. Complete the following derivations in SD.
(a)(10%) Derive N
1│C v F Assumption
2│C≡N Assumption
3│F⊃N Assumption
├───
│
(b)(10%) Derive G⊃(H⊃I)
1│(G＆H)⊃I Assumption
├─────
│
(c)(10%) Derive ~B
1│~(A v B) Assumption
├────
│
8. Find and explain each mistake in following attempted truth-tree
or derivation:
(a)(5%) 1. (A⊃~B)⊃(B v C) SM
2. ~(B v C) SM
3. ~B 2~vD
4. ~C 2~vD
／＼
／ ＼
5. ~(A⊃~B) B v C 1⊃D
6. A │ 5~⊃D
7. B ／＼ 5~⊃D
╳ ／ ＼
8. B C 5vD
╳ ╳
(b)(5%) Derive: A
1│~(A⊃~A) Assumption
├────
2││~A A/~E
│├──
3│││A A/~I
││├─
4│││~A 2R
5│││A 3R
6││~A 3-5 ~I
7││A 3 R
8│A 2-7 ~E