01204211/activity1 logic1

In-class activities

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

1.1 It is raining or it is very hot.

1.2

1.3

1.4

2. 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)

2.1 Every human must die.

2.2 Some animal eats other animals.

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

2.4 Everyone has someone that care about him or her.

2.5 There is someone that everyone cares about.

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

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