01204211/activity1 logic1

In-class activities

1.

2. For each of these sentences, define appropriate propositional variables representing each proposition inside the statement and translate the statement into a propositional form.

2.1 It is raining or it is very hot.

2.2 If you like Thai food, you will enjoy the trip to the Night Market.

2.3 The only way you can finish a marathon is that you practice a lot and have strong will to fight.

2.4 You either learn to understand the customer or you fail to make a good product.

3. Quantifiers. Consider the universe to be "everything." For each of these statements, define appropriate predicates can rewrite the statement using the defined predicates and quantifiers. (Some predicate may have more than one variables)

3.1 Every human must die.

3.2 Some animal eats other animals.

3.3 If a student works hard, that student will be successful.

For questions 3.4 and 3.5, consider the universe to be a set of all people.

3.4 Everyone has someone that care about him or her.

3.5 There is someone that everyone cares about.

For questions 3.6 and 3.7, consider the universe to be a set of all companies.

3.6 When the economy is good, any companies can make good profits.

3.7 When the economy is bad, only companies that can adapt survive.

4. It seems that universal quantifiers are stronger than existential ones. Is it true that for any set $A$ and predicate $P(x)$,

$(\forall x\in A,P(x))\Rightarrow (\exists x\in A,P(x))$?