2.4 Deductive Reasoning

(mathxl 2.4.11) Use the Law of Syllogism to make a conclusion, if possible.

If we cooperate, then we'll get the job done faster.

If we get the job done faster, then we can go to a movie.

• If we can go to a movie, then we'll cooperate.

• If we don't cooperate, then we can't go to a movie.

• If we cooperate, then we can go to a movie.

• None of the conclusions are valid because neither conclusion of the conditional statements is the hypothesis of the other statement.

(mathxl 2.4.13)

If possible, use the Law of Syllogism to make a conclusion.

If you want to play cards, then we'll play poker.

If we play poker, then we'll play Texas Hold'em.

• If you want to play cards, then we'll play Texas Hold'em.

• If we play Texas Hold'em, then you want to play cards.

• If you don't want to play cards, then we won't play Texas Hold'em.

• None of the conclusions are valid because neither conclusion of the conditional statements is the hypothesis of the other statement.

(mathxl 2.4.6)

If possible, use the Law of Detachment to make a conclusion.

If the band plays, then the people are happy.

The band does not play.

• The conclusion is the band does not play.

• The conclusion is the band plays.

• The conclusion is the people are not happy.

• It is not possible to make a conclusion using the Law of Detachment because the second statement does not match the hypothesis of the given conditional.