1) Let p, q, and r be the propositions p: Phyllis goes out for a walk. q: The mo
ID: 3663232 • Letter: 1
Question
1) Let p, q, and r be the propositions p: Phyllis goes out for a walk. q: The moon is out. r: It is raining. Express each of these propositions as an English sentence.
(a) ¬r q.
(b) ¬q r.
(c) q ¬r.
(d) (q ¬r) p.
(e) (p ¬r)(q ¬r)
(f) (pq)(¬qr).
2) State the converse, contrapositive, and inverse of each of these conditional statements. (a) If it snows today, I will ski tomorrow. (b) I come to class whenever there is going to be a quiz. (c) A positive integer is a prime only if it has no divisors other than 1 and itself.
3) Rewrite each of the following statements as an implication in the if-then form. (a) Practicing her serve daily is a sufficient condition for Darci to have a good chance of winning the tennis tournament. (b) Fix my air conditioner or I won't pay the rent. (c) Mary will be allowed on Larry's motorcycle only if she wears her helmet.
4) Use truth tables to verify the distributive laws (a) p (q r) (p q) (p r) (b) p (q r) (p q) (p r) 5) Verify that [p (q r)] [(p q) (p r)] is a tautology
Explanation / Answer
Consider 1=True and 0 =False for the following truth tables
4) Use truth tables to verify the distributive laws
(a) p (q r) (p q) (p r)
(b) p (q r) (p q) (p r)
5) Verify that [p (q r)] [(p q) (p r)] is a tautology
p q r pvq pvr (pvq) ^ (pvr) q^ r p v (q ^ r) 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1Related Questions
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