Predicate Logic

Question 1

Existential Quantifier

Answer 1

∃, “for some” or “there is” or “there exists”

Question 2

Universal Quantifier

Answer 2

∀, “every” or “all” or “each”

Question 3

∀ and ∃ Equivalence

Answer 3

∃x is equivalent to ¬∀x¬

∀x is equivalent to ¬∃x¬

Question 4

Individual constants

Answer 4

a, b, c etc.

Question 5

Individual variables

Answer 5

x, y, z etc.

Question 6

Predicate letters

Answer 6

P, Q, R etc.

Question 7

Function symbols

Answer 7

f, g, h etc.

Question 8

Term

Answer 8

Expressions referring to individual objects, e.g. individual constants, individual variables, functions

Question 9

Formula

Answer 9

Terms, terms with propositional connectives, formula

Question 10

Ground term

Answer 10

A term which contains no variables and is constructed entirely from constants and function symbols

Question 11

Bound

Answer 11

All occurrences of x in a quantified formula ∀xα or ∃xα are said to be bound

Question 12

Free

Answer 12

Any occurrence of a variable that is not bound is said to be free

Question 13

Closed formula

Answer 13

A formula containing no free variables is said to be closed

Question 14

Open formula

Answer 14

A formula containing at least one free variable is said to be open

Question 15

And-introduction

Answer 15

From φ and ψ you can infer φ ∧ ψ

Question 16

And-elimination

Answer 16

From φ ∧ ψ you can infer both φ and ψ

Question 17

Or-introduction

Answer 17

From φ you can infer both φ ∨ ψ and ψ ∨ φ

Question 18

Or-elimination

Answer 18

If you can infer χ both from φ and from ψ, then you can infer χ from φ ∨ ψ

Question 19

If-introduction

Answer 19

If you can infer ψ from φ, then you can prove φ → ψ

Question 20

If-elimination

Answer 20

From φ and φ → ψ you can infer ψ