Elementary Propositional Logic

Problem1

Which of the following propositions are true? (Select all that are.)

(Q1)

? A: 1+1=2 B: 4 is prime & the Earth is closer to the Moon than to the Sun C: (1)(1)<1 D: 4 is prime | 3 is an even integer

Which of the following propositions are true? (Select all that are.)

(Q2)

? A: 3 is an odd integer & 4 is a perfect square B: the Earth is closer to the Moon than to the Sun | (1)(1)<1 C: 3 is an even integer & the Moon is made of cheese D: 4 is a perfect square | the Earth is closer to the Moon than to the Sun

Which of the following propositions are true? (Select all that are.)

(Q3)

? A: 3 is an even integer the Earth is closer to the Moon than to the Sun B: 4 is prime 3 is an even integer C: 4 is a perfect square 1+1=2 D: 4 is prime 1+1=2

Which of the following propositions are true? (Select all that are.)

(Q4)

? A: 1+1=2 4 is prime B: the Moon is made of cheese (1)(1)<1 C: 3 is an odd integer !(the Earth is closer to the Moon than to the Sun) D: 4 is a perfect square (1)(1)<1

Problem2

Fill in the following truth table:

Truth Tablepqp | ( !q & !p ) TT (Q5)

? A: T B: F

TF (Q6)

? A: T B: F

FT (Q7)

? A: T B: F

FF (Q8)

? A: T B: F

Problem3

Fill in the following truth table:

Truth Tablepq!p !q TT (Q9)

? A: T B: F

TF (Q10)

? A: T B: F

FT (Q11)

? A: T B: F

FF (Q12)

? A: T B: F

Problem4

What is the structure of the following argument?

If the Sun orbits the Earth or the Moon is made of cheese, then Homer Simpson is an alien; Homer Simpson is an alien. Therefore, either the Sun orbits the Earth or the Moon is made of cheese. (Q13)

? A: p q; q r; r s; p. Therefore, s.B: p | q; !p. Therefore, q.C: (p | q) r; !r. Therefore, !p & !q.D: (p | q) r; r. Therefore, p | q. E: p q; q r; r s; !s. Therefore, !p. F: p & q. Therefore, p | q.G: p q; p. Therefore, q.H: p q; !p. Therefore, !q.

Is the argument logically valid? (Q14)

? A: no B: yes

Problem5

Which of the following are valid logical arguments? (Select all that are.)

(Q15)

? A: p & q. Therefore, p. B: p | q; !q. Therefore, p. C: (p & q) r; !r. Therefore, !p & !q. D: p q; p r; r. Therefore, q.

Which of the following are valid logical arguments? (Select all that are.)

(Q16)

? A: (p | q) r; p !q; r. Therefore, q.B: p q; !q. Therefore, !p. C: p q; p r; r. Therefore, q.D: p q; !p. Therefore, !q.

Which of the following are valid logical arguments? (Select all that are.)

(Q17)

? A: p | q | r. Therefore, p | q. B: (p & q) r; !r. Therefore, !p | !q.C: p q; q. Therefore, p. D: r (p | q); p !q; r. Therefore, (p & !q) | (q & !p).

Which of the following are valid logical arguments? (Select all that are.)

(Q18)

?A: p q. Therefore, p q.B: (p & q) | r. Therefore, (p & r) | (q & r).C: p q. Therefore, (p & q) | (!p & !q). D: (p & q) | (!p & !q). Therefore, p q.