2.7 Logical Arguments

Detachment, denying the consequent, and the chain rule as the three patterns for drawing a valid conclusion from a pair of true premises.

Contemporary Mathematics, 2.7 Logical Arguments

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3 exercises

2.7 Exercise 1

Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine a valid conclusion.

If Leonardo da Vinci was an artist, then he painted the Mona Lisa. Leonardo da Vinci was an artist.
If Michael Jordan played for the Chicago Bulls, then Michael Jordan was not a soccer player. Michael Jordan played for the Chicago Bulls.
If a…

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2.7 Exercise 3

Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine a valid conclusion.

If Leonardo da Vinci was an artist, then he painted the Mona Lisa. Leonardo da Vinci did not paint the Mona Lisa.
If Michael Jordan played for the Chicago Bulls, then Michael Jordan was not a soccer player. Michael Jordan was a so…

2.5

2.7 Exercise 5

Each pair of statements represents true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.

If my roommate goes to work, then my roommate will get paid. If my roommate gets paid, then my roommate will pay their bills.
If robins can fly, then some birds can fly. If some birds can fly, then we will watch…

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