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.
A Exercise is healthy
B Heart attacks indicate heart disease
C Regular exercise prevents heart attacks
D All of the above
Explanation: If heart attacks indicate heart disease, the lower rate among exercisers strengthens the claim.
A C is true
B C is false
C C is unknown
D B is false
Explanation: By transitivity of equivalence, if A↔B↔C and A is true, C is true.
A All doctors are happy
B Some doctors earn more
C No doctors are happy
D All happy people are doctors
Explanation: Since some doctors specialize and all specialists earn more, some doctors earn more.
A Green spaces provide nature
B Nature reduces stress
C Stress affects mental health
D All of the above
Explanation: For the argument to hold, all three assumptions must be true.
A P is true and Q is true
B P is false and Q is true
C P is true and Q is false
D Both P and Q are false
Explanation: Since R is false and exactly 2 are true, both P and Q must be true. P→Q holds.
A All tropical fruits are hardy
B Some tropical fruits may be hardy
C No tropical fruits are hardy
D All hardy things are tropical fruits
Explanation: We can only conclude that some tropical fruits may be hardy.
A Attention helps learning
B Teacher quality matters more than class size
C Students need attention
D Education is important
Explanation: If teacher quality matters more, class size alone may not improve education.
A P is true
B Q is true
C P is false
D R is false
Explanation: Q→S and S is false means Q is false. P→Q and Q is false means P is false.
A All engineers are brilliant
B Some engineers are not average
C No engineers are average
D All average people are engineers
Explanation: Since some engineers study physics and some physics students are brilliant, some engineers may be brilliant and therefore not average.
A Renewable energy reduces emissions
B Emissions cause climate change
C We should invest in renewables
D Climate change is bad
Explanation: The recommendation to invest in renewables is the conclusion supported by the premises.
A A is true
B C is true
C A is false
D Both B and C are true
Explanation: A∧C→D and D is false means A∧C is false. Since B is true, for A∧B→C, if C is false then A must be false.
A All birds are beautiful
B Some birds may be beautiful
C No birds are beautiful
D All beautiful things are birds
Explanation: We can only conclude that some birds may be beautiful.
A Literacy indicates education
B Lower poverty is better
C Education is accessible
D All of the above
Explanation: If literacy rates indicate education levels, the correlation strengthens the causal claim.
A B and C are true
B B is true, C is unknown
C C is true, B is unknown
D B and C are false
Explanation: By chaining, A→B→C→A. If A is true, B is true, C is true, and back to A.
A All students inspire others
B Some students may inspire others
C No students inspire others
D All inspiring people are students
Explanation: We can only conclude that some students may inspire others.