Symbolic Logic Translations

Symbolic Logic Translations

• The subject matter of an argument is irrelevant to its validity.
• Formal notation allows us to determine validity in a more rigorous manner.

Symbolic Logic Translations

• Sentences can be parts of other sentences.
   

1. Whales are mammals.
2. Whales are mammals and humans are mammals.

Symbolic Logic Translations

• Sentences can be parts of other sentences.
   

1. Whales are mammals.
2. Whales are mammals or birds can fly.

Symbolic Logic Translations

• Atomic Sentence: A sentence that does not have any other sentences as parts.
• Complex sentence: A sentence that does has other sentences as parts.

Symbolic Logic Translations

To translate into symbolic notation:

1. Identify all atomic sentences.
2. Assign a unique variable for each unique sentence.
3. Replace all atomic sentences with their corresponding variable.

Symbolic Logic Translations

p: Alice is tall

q: Bob is short

1. Alice is tall or Bob is short.
2. Alice is not tall.
3. Therefore, Bob is short.

1. p or q
2. Not p
3. q

Symbolic Logic Translations

p: All whales are mammals

q: Willy is whale

r: Willy is a mammal

If all whales are mammals and Willy is a whale, then Willy is a mammal.

• If p and q, then r

Not p

p and q

p or q

If p then q

p if q

p only if q

p unless q

p if and only if q

~p

p & q

p V q

p -> q

q -> p

p -> q

~q -> p

p <-> q

Symbolic Logic Translations

Symbolic Logic Translations

p: Alice is tall

q: Bob is short

1. Alice is tall or Bob is short.
2. Alice is not tall.
3. Therefore, Bob is short.

1. p or q
2. Not p
3. q

1. p V q
2. ~p
3. q

Symbolic Logic Translations

Key Concepts

• Atomic Sentences
• Complex Sentences
• Logical Connectives