Answer to Question #222300 in Discrete Mathematics for Chan

Question

ACTIVITIES/ASSESSMENT:

A. Tell if the following statements are propositions or not.

1. Study hard!

2. The Apple Macintosh is a 16-bit computer.

3. 1 is an even number.

4. Why are we here?

5.8+7=13

B. p is "x < 50", q is "x > 40". Write the following in words.

1. ~P

2. ~q

3. p^ q

4. pv q 5. ~p ^ q

6. ~p~q

C. Construct a truth table for the following:.

1. PA (QVR) 2. (Ρ Λ Ω) v R

3. (PA~Q) V ~P 4. P→ (Q V~R)

5. [(PQ) v (P→ R)]

Answer 1

A.

1. It is not a proposition.
2. It is a proposition.
3. It is a proposition.
4. It is not a proposition.
5. strictly speaking is a propositional function, but many people would say it is a proposition.

B.

1. x ≥ 50
2. x ≤ 40
3. 40 < x < 50
4. x < 50 or x > 40. This is true for all values of x
5. x ≥ 50 (Note that we don't need to say, in addition, that x > 40; this must be true whenever x ≥ 50)
6. x ≥ 50 and x ≤ 40. This can never be true, whatever the value of x

C.

P ^ (QVR)

(Ρ Λ Ω) v R

(PA~Q) V ~P

P→ (Q V~R)

For 5., Operation between P and Q is not clearly specified here.