Avoiding Fallacious Reasoning: Lesson 6

The following exercises were taken from LogicCola, which is software written by a logic professor, Dr. Harry Gensler. These are considered very easy, and they should be mastered before moving on in the next lesson.

Some basic rules in a clause:

If negation comes first in the clause, then put the tilde outside of the parenthesis. The tilde is the main operator of the clause

If either comes first, then the wedge is the main operator of the clause

If both comes first, then the conjunction is the main operator


Both P and either L or F

(P • (L V F))

1 translation: You aren’t both not scholarly and frivolous

2 translation: If C then F, or P

3 translation: If not W then P

4 translation: You’re dull, and cowardly or faithful

5 translation: Either both S and N or C

6 translation: Either not R or not G

7 translation: You’re both smart and either candid or beautiful

8 translation: Not if not S then G

9 translation: If you’re clean, then you’re lonely and humorous

10 translation: It’s false that if you’re cruel then you’re logical

11 translation: If you’re mean then you’re nervous, and you’re persistent

12 translation: Not either R or D

13 translation: Either not R or B

14 translation: Not either not W or T

15 translation: You aren’t both generous and prosperous

16 translation: You’re strong and realistic, or else powerful

17 translation: Both not R and not L

18 translation: You’re both not faithful and bitter

19 translation: If you’re dull and filthy, then you’re greedy

20 translation: You’re poor, and confident or beautiful

21 translation: You aren’t both not selfish and loveable

22 translation: If W then C, or H

23 translation: Both S and either N or P

24 translation: If you’re clean, then you’re demented or bashful

25 translation: It is false that if you aren’t dull then you’re boring

26 translation: Not either P or T

27 translation: Either both R and C or F

28 translation: You’re either not rough or else gentle

Answers to Lesson 6

1 answer: ~(~S • F)
2 answer: ((C ɔ F) V P)
3 answer: (~W ɔ P)
4 answer: (D • (C V F))
5 answer: ((S • N) V C)
6 answer: (~R V ~G)
7 answer: (S • (C V B))
8 answer: ~(~S ɔ G)
9 answer: (C ɔ (L • H))
10 answer: ~(C ɔ L)
11 answer: ((M ɔ N) • P)
12 answer: ~(R V D)
13 answer: (~R V B)
14 answer: ~(~W V T)
15 answer: ~(G • P)
16 answer: ((S • R) V P)
17 answer: (~R • ~L)
18 answer: (~F • B)
19 answer: ((D • F) ɔ G)
20 answer: (P • (C V B))
21 answer: ~(~S • L)
22 answer: ((W ɔ C) V H)
23 answer: (S • (N V P))
24 answer: (C ɔ (D V B))
25 answer: ~(~D ɔ B)
26 answer: ~(P V T)
27 answer: ((R • C) V F)
28 answer: (~R V G)