extra credit, quiz #2

 Translate into formal language and show validity:

If you want to avoid silly errors in life or maximize your intellectual potential, then you should choose to study logic. No doubt you do want to maximize your intellectual potential and be the best student you can be. If you do choose to study logic, then you will be in charge of your life.  Therefore, you will indeed be in charge of your life.  (Use A, M, L, B and C)

Assignment #6: Formal Methods II: Categorical Logic

1. Read Van Cleave, section 2.14; do exercise set 18.

2. Read 2.17; do exercise set 21.

Practice Quiz #2

 We will review this practice quiz on Monday, March 23; we will have quiz #2 on Wednesday, March 25

1. Reproduce the chart for induction and deduction.

2. Write a sound deductive inference.

3. Write a strong inductive inference.

4. Translate into formal symbolic language:

a. I will go to the party only if you will go (use I and Y).

b. It is not both sunny and warm today (use S and W).

c. It is neither sunny nor warm today (use S and W)

5. Is the following inference valid or invalid:

If A then B; not A, therefore, not B.

Show validity using the 8 rules of deduction:

1. Q

2. P   /therefore, (Q or R) and P

1. If A then B

2. not B and not C  /therefore, not A and not C

1. If D or E, then A and B

2. D   /therefore, B

1. If P then Q

2. P or (R and S)  

3. not Q and not T   /therefore, R

Translate and show validity using the 8 rules of deductive reasoning:

If you care about your education, you will succeed; and if you succeed, your years at MCLA will be spent wisely. You do care about your education, and you will either fail to spend your years at MCLA wisely or you will reap one of life's greatest rewards. It follows that you will reap that reward. (use C, S, Y, R)

Assignment #5: Formal Proofs

Read: Van Cleave, section 2.11. Do exercise sets 16 & 17.

8 Rules of valid inference:

Modus Ponens (MP)

p⊃q,
p
∴
q

 Modus Tollens (MT)

 p⊃q,
~q
∴
~p

 Disjunctive Syllogism (DS)

p∨q,
~p
∴
q

 or, if desired,

p∨q,
~q
∴
p

Simplication (Simp)

p.q
∴
p

 or, if desired,

p.q
∴
q

Conjunction (Conj)

p,
q
∴
p.q

Hypothetical Syllogism (HS)

p⊃q,
q⊃r
∴
p⊃r

Addition(Add)

 p

∴
p∨q

 Constructive Dilemma (CD)

(p⊃q),
(r⊃s),
p∨r
∴
q∨s