Question

1. Given the following predicates and premises: C(x): “ x is in this class” R(x): “ x owns a yellow truck” T(x): “ x has gotten a parking ticket.” Premises C(Linda), R(Linda) , ∀x(R(x) → T(x)) Conclude that ∃x(C(x) ∧ T(x))

2.Find the error/s in this argument that shows that if ∃xP(x) ∧ ∃xQ(x) is true then ∃x(P(x) ∧ Q(x)) is true.

1. ∃xP(x) ∧ ∃xQ(x) Premise

2. ∃xP(x) Simplification from (1)

3. P(c) Existential instantiation from (2)

4. ∃xQ(x) Simplification from (1)

5. Q(c) Existential instantiation from (4)

6. P(c) ∧ Q(c) Conjunction from (3) and (5)

7. ∃x(P(x) ∧ Q(x)) Existential generalization

Answer 1

Q1.

We have been given that:

1. C(Linda) (Premise)
2. R(Linda) (Premise)
3. ∀x(R(x) → T(x)) (Premise)
4. T(Linda)   (Universal Modus Ponens on (3) and (2))
5. C(Linda) ∧ T(Linda) (Conjunction of (1) and (4))
6. ∃x(C(x) ∧ T(x)) (Existential generalization of (5))

Q.E.D.

• Premises are the statements that are provided and are known to be true.
• Modus Ponens states that:

if (R(x) → T(x)) for all x

& R(c) is true for some constant c then,

T(c) is also true.

• Conjunction implies that :

If T(x) is true and C(x) is also true then,

C(x) ∧ T(x) is also true for any x

• Existential generalization states that if:

A(k) is true for some constant k then,

A(x) is also true for some x OR ∃x(A(x)) is true

(Thank You!)