Chapter 1: Q17E (page 35)
Show thatandare logically equivalent
The truth value both statements are same, it is prove that statement and are logically equivalent
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Construct a truth table for each of these compound propositions.
Let andbe the statements “xis a baby,” “xis logical,” “xis able to manage a crocodile,” and “xis despised,” respectively. Suppose that the domain consists of all people. Express each of these statements using quantifiers; logical connectives; andand.
a) Babies are illogical.
b) Nobody is despised who can manage a crocodile.
c) Illogical persons are despised.
d) Babies cannot manage crocodiles.
e) Does (d) follow from (a), (b), and (c)? If not, is there a correct conclusion?
Let and be the statements “xis a duck,” “xis one of my poultry,” “xis an officer,” and “xis willing to waltz,” respectively. Express each of these statements using quantifiers; logical connectives; andand.
(a) No ducks are willing to waltz.
(b) No officers ever decline to waltz.
(c) All my poultry are ducks.
(d) My poultry are not officers.
(e) Does (d) follow from (a), (b), and (c)? If not, is there a correct conclusion?
Write each of these propositions in the form “p if and only if q” in English.
a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.
b) For you to win the contest it is necessary and sufficient that you have the only winning ticket.
c) You get promoted only if you have connections, and you have connections only if you get promoted.
d) If you watch television your mind will decay, and conversely.
e) The trains run late on exactly those days when I take it.
Let and be the statements “xis a clear explanation,” “xis satisfactory,” and “xis an excuse,” respectively. Suppose that the domain for x consists of all English text. Express each of these statements using quantifiers, logical connectives, and and .
a) All clear explanations are satisfactory.
b) Some excuses are unsatisfactory.
c) Some excuses are not clear explanations.
d) Does (c) follow from (a) and (b)?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
