question archive Basic Ideas and Tools a) ~(Av~B) b) (D&~G)v(G&D) c) [(DV~~B)&(DVB)]&(DVB) d) L&Mv[~N&(MV-L)]} 1-6
Basic Ideas and Tools a) ~(Av~B) b) (D&~G)v(G&D) c) [(DV~~B)&(DVB)]&(DVB) d) L&Mv[~N&(MV-L)]} 1-6
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Basic Ideas and Tools a) ~(Av~B) b) (D&~G)v(G&D) c) [(DV~~B)&(DVB)]&(DVB) d) L&Mv[~N&(MV-L)]} 1-6. RULES OF FORMATION AND RULES OF VALUATION We can summarize many important points discussed so far by giving ex- plicit rules which tell us what counts as a sentence of sentence logic and how to determine the truth values of compound sentences if we are given the truth values of the components: Formation Rules i) Every capital letter 'A', 'B', 'C' . . . is a sentence of sentence logic. Such a sentence is called an Atomic Sentence or a Sentence Letter. ii ) If X is a sentence of sentence logic, so is (~X), that is, the sentence formed by taking X, writing a '~' in front of it, and surrounding the whole by parentheses. Such a sentence is called a Negated Sentence.
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a) ~(A v ~B)
| Sentence | Main Connective | Components |
| a) ~(A v ~B) | ~ | A v ~B |
| A v ~B | v | A, ~B |
| ~B | ~ | B |
b. (D & ~G) v (G &D)
| Sentence | Main Connective | Components |
| b) (D & ~G) v (G &D) | v | (D & ~G), (G &D) |
| D & ~G | & | D, ~G |
| ~G | ~ | G |
| G &D | & | G, D |
c. [(D v ~~B) & (D v B)] & (D v B)
| Sentence | Main Connective | Components |
|
c) [(D v ~~B) & (D v B)]&(D v B)
|
& | [(D v ~~B) & (D v B)], (D v B) |
| [(D v ~~B) & (D v B)] | & | (D v ~~B), (D v B) |
| (D v ~~B) | v | D, ~~B |
| ~~B | ~ | ~B |
| ~B | ~ | B |
| (D v B) | v | D, B |
d. L & [M v [~N & (M v ~L)]]
| Sentence | Main Connective | Components |
|
d) L & [M v [~N & (M v ~L)]]
|
& | L, [M v [~N & (M v ~L)] |
| [M v [~N & (M v ~L)] | v | M, [~N & (M v ~L)] |
| [~N & (M v ~L)] | & | ~N, (M v ~L) |
| ~N | ~ | N |
| (M v ~L) | v | M, ~L |
| ~L | ~ | L |
Step-by-step explanation
16. Basic Ideas and Tools
a) ~(A v ~B)
| Sentence | Main Connective | Components |
| a) ~(A v ~B) | ~ | A v ~B |
| A v ~B | v | A, ~B |
| ~B | ~ | B |
b. (D & ~G) v (G &D)
| Sentence | Main Connective | Components |
| b) (D & ~G) v (G &D) | v | (D & ~G), (G &D) |
| D & ~G | & | D, ~G |
| ~G | ~ | G |
| G &D | & | G, D |
c. [(D v ~~B) & (D v B)] & (D v B)
| Sentence | Main Connective | Components |
|
c) [(D v ~~B) & (D v B)]&(D v B)
|
& | [(D v ~~B) & (D v B)], (D v B) |
| [(D v ~~B) & (D v B)] | & | (D v ~~B), (D v B) |
| (D v ~~B) | v | D, ~~B |
| ~~B | ~ | ~B |
| ~B | ~ | B |
| (D v B) | v | D, B |
d. L & [M v [~N & (M v ~L)]]
| Sentence | Main Connective | Components |
|
d) L & [M v [~N & (M v ~L)]]
|
& | L, [M v [~N & (M v ~L)] |
| [M v [~N & (M v ~L)] | v | M, [~N & (M v ~L)] |
| [~N & (M v ~L)] | & | ~N, (M v ~L) |
| ~N | ~ | N |
| (M v ~L) | v | M, ~L |
| ~L | ~ | L |
References
Pospesel, H., & Lycan, W. G. (1998). Introduction to logic: Propositional logic (3rd ed.).
