Key info for midterm

Question 1

If a schema is a conjunction of sentence letters and negations of sentence letters, then it is satisfiable if and only if ___

Answer 1

No sentence letter occurs as a conjunct both unnegated and negated

Question 1

A disjunction is satisfiable if and only if ___

Answer 1

At least one of its disjuncts is satisfiable

Question 2

True of false: If both X and Y are satisfiable, then X ∨ Y is satisfiable

Answer 2

False, not necessarily

Proof that it’s not true requires a concrete counter-example that is usually very simple

Question 3

Existential quantifier uses what connective?

Answer 3

Conjunction

Question 4

Universal quantifier uses what connective?

Answer 4

Conditional

Question 5

Existential and universal quantifier equivalences

Answer 5

(∃x) can be replaced with ¬(∀x)¬

(∀x) can be replaced with ¬(∃x)¬

Question 6

Negation of ‘some philosophers are wise’

Answer 6

No philosopher is wise/all philosophers are unwise

Question 7

Negation of ‘some philosophers are unwise’

Answer 7

All philosophers are wise (no philosophers are unwise)

Question 8

What does equivalence preserve?

Answer 8

• Validity
• Unsatisfiability
• Implication
• Equivalence
• Satisfiability

Question 9

What does substitution preserve?

Answer 9

• Validity
• Unsatisfiability
• Implication
• Equivalence
• NOT SATISFIABILITY

Question 10

De Morgan Laws

Answer 10

¬(𝑃∨𝑄) is (¬𝑃∧¬𝑄) and vice versa

¬(𝑃∧𝑄) is (¬𝑃∨¬𝑄) and vice versa