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rolo7105
rolo7105
04.02.2020 • 
Mathematics

Tip #1: put the if-part first and the then-part second.

so, (q, if p) = (if p, then q)

for example, (i sleep, if i’m tired) = (if i’m tired, then i sleep)

tip #2: only if = then

so, (p only if q) = (if p, then q)

for example, mary drinks cola only if it is pepsi = if mary drinks cola, then it is pepsi.

tip #3: unless = if-not

so, (p unless q) = (p, if-not q) = (if-not q, then p)

for example, mary drinks cola unless it is coke = if it is not coke, then mary drinks cola.

question 1:

a. translate the following statements to their corresponding symbolic expressions. be sure to use statement indicators and connective indicators in your translation to produce conditional statements. a translation key must be provided for each exercise (see above for an example).

1) if it is raining, then jack will not go to the baseball game.

2) i eat, if i’m hungry.

3) jack watches football on t.v. only if the ohio state team is playing.

4) janet plays with weird pets unless it is a tarantula.

5) when i watch a baseball game, i eat several hot dogs.

b. for these five statements above, identify the antecedent and the consequent for each conditional.

question 2:

construct a valid deductive arguments by applying the five argument forms (rules) on the worksheet below. you will need to insert your own example for each rule, following the form of the argument. a translation key must be provided for each exercise (see above for an example).

forms/rules:

modus ponens

1) if p, then q.

2) p.



3) thus, q.

modus tollens

1) if p, then q.

2) not q.



3) thus, not p.

hypothetical syllogism

1) if p, then q.

2) if q, then r.



3) thus, if p, then r.

disjunctive syllogism

1) p or q.

2) not p.



3) thus, q.

dilemma

1) p or q.

2) if p, then r.

3) if q, then s.



4) thus, r or s.

your examples for each form/rule above:

question 3:

1. answer the question: what is the advantage of translating verbal arguments to symbolic argument forms?

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