A P is true
B Q is true
C P is false
D Q is unknown
Explanation: By modus tollens backwards, ¬R implies ¬Q, and ¬Q implies ¬P.
A Sarah is a doctor
B Sarah is a lawyer
C Sarah might be a doctor or lawyer
D Sarah is neither
Explanation: Having a degree is necessary but not sufficient for being a doctor or lawyer.
A Self-paced learning is effective
B Online learning enables self-pacing
C Students benefit from flexibility
D All of the above
Explanation: The argument requires all these assumptions for the conclusion to follow.
A B is true
B A is true
C B is false
D A is unknown
Explanation: If A is sufficient for C and C is true, A must be true.
A All reptiles are dangerous
B Some reptiles may be dangerous
C No reptiles are dangerous
D All dangerous animals are reptiles
Explanation: We can only conclude that some reptiles may be dangerous.
A Businesses hire based on need
B Some businesses absorb cost increases
C Unemployment is bad
D Workers need fair pay
Explanation: If businesses absorb cost increases rather than cutting jobs, the unemployment claim is weakened.
A A is true
B B is true
C C is true
D All of A-D are false
Explanation: By modus tollens backwards, if E is false, then D, C, B, and A must all be false.
A No fiction is mathematics
B Some books are not mathematics
C All mathematics is fiction
D Both A and B
Explanation: Since fiction requires imagination and math doesn\'t, no fiction is math. And since some books are fiction, some books are not math.
A Renewable costs are decreasing
B Cost is the main barrier
C Fossil fuels will become obsolete
D All of the above
Explanation: The argument requires all these assumptions for the prediction to be valid.
A P must be false
B Q must be true
C R must be true
D P is true and Q is true
Explanation: If P→Q and only one is true, P cannot be true (otherwise Q would also be true, violating the one-true condition).
A All roses need water
B All roses need sunlight
C Some roses need water and sunlight
D All of the above
Explanation: Since some flowers are roses and all flowers need water and all plants need sunlight, all roses need both.
A Ban cars because one person was in an accident
B Regulate cars because accidents cause injuries
C Ignore cars because most drivers are safe
D Ban all transportation
Explanation: A balanced argument acknowledging both risk and necessity is stronger than extremes.
A B is true
B B is false
C A is false
D Both are true
Explanation: If A∨B is true but A∧B is false, they can\'t both be true. Since A is true, B must be false.
A All countries have healthier populations
B Some countries have healthier populations
C No countries have healthier populations
D Universal healthcare causes poor health
Explanation: Since some countries have universal healthcare and all such countries have healthier populations, some countries have healthier populations.
A Space exploration produces technology
B Technology benefits Earth
C The benefits outweigh costs
D All of the above
Explanation: For the argument to work, all these assumptions must hold.
A P is true
B P is false
C Contradiction
D Q is false
Explanation: R→¬P and R is true means P is false. This is consistent with P→Q where Q is true.
A All students are open-minded
B Some students are open-minded
C No students are open-minded
D All open-minded people studied abroad
Explanation: By chained syllogisms, some students study abroad and become open-minded.
A Reflexes are important
B Gamers may have better reflexes before gaming
C Reaction tests measure reflexes
D Video games are popular
Explanation: If gamers already had better reflexes before gaming, the causal claim is weakened.
A B is true
B B is false
C A is false
D Both B and C are true
Explanation: A→B and A is true means B is true. But B→C and C is false means B is false. Contradiction implies something is wrong.
A All penguins lay eggs
B Some penguins lay eggs
C No penguins lay eggs
D All egg-layers are penguins
Explanation: By syllogism, all penguins are birds, all birds have feathers, all feathered creatures lay eggs, so all penguins lay eggs.