9 Ninth Week

Question 1

Describe the introduction rule for the existential quantifier.

Answer 1

You can infer an existential generalization from any instance. For example, you can infer ∃x Fx from Fa.

Question 2

Describe the elimination rule for the existential quantifier.

Answer 2

The basic idea behind this rule is simple. Given an existential statement (e.g. ∃x Fx) you can introduce a name for a witness (e.g. Fi). It’s important that you choose a new name — i.e. a name that doesn’t otherwise appear in the proof, or in the inference you’re trying to prove.

Sadly, the formatting for the rule is tricky!

Question 3

Symbolize the statement “Some beetle has spots”.

UD: Animals
Bx: x is a beetle.
Sx: x has spots

Answer 3

∃x(Bx ^ Sx)

Question 4

Symbolize the statement “Some beetle doesn’t have spots”.

UD: Animals
Bx: x is a beetle.
Sx: x has spots

Answer 4

∃x(Bx ^ ~Sx)

Question 5

True or False: In this course, we insist that the domain must always be non-empty.

Answer 5

True.