A Physical activity improves mental health
B Schools should require exercise
C Mental health is important
D Schools have authority
Explanation: The recommendation for schools to require exercise is the conclusion.
A Contradiction
B B is false
C A is false
D C is true
Explanation: A∧B→C and both A and B are true means C should be true. But C is false, creating a contradiction.
A All scholarship recipients have great careers
B Some scholarship recipients may have great careers
C No scholarship recipients have great careers
D All great careers come from scholarships
Explanation: We can only conclude that some scholarship recipients may have great careers.
A Gene therapy is innovative
B Root cause targeting may have side effects
C Curing diseases is good
D Technology is advancing
Explanation: If targeting root causes has side effects, the cure may come with new problems.
A Q is true
B R is true
C S is true
D All of Q-U are false
Explanation: By modus tollens backwards, if V is false, then U, T, S, R, and Q must all be false.
A All imported fruits create waste
B Some imported fruits may create waste
C No imported fruits create waste
D All waste comes from imported fruits
Explanation: All imported fruits travel long distances, which requires packaging, which creates waste.
A Volunteering is popular
B Life satisfaction indicates better mental health
C Mental health is important
D Volunteers are happy people
Explanation: If life satisfaction indicates better mental health, this strengthens the claim.
A B is false
B D is false
C Both B and D are false
D A is false
Explanation: A∧B→C and C is false means A∧B is false. Since A is true, B is false. A∧D→E and E is false means A∧D is false. Since A is true, D is false.
A All exchange students are creative
B Some exchange students may be creative
C No exchange students are creative
D All creative people are exchange students
Explanation: We can only conclude that some exchange students may be creative.
A Travel is a barrier
B Not traveling improves access
C Access matters
D All of the above
Explanation: For the argument to hold, all these assumptions must be true.
A A is true
B B is true
C C is true
D All of the above
Explanation: D→A and D true means A true. D→B and D true means B true. A∧B→C means C true.
A All oil-producing countries generate revenue
B Some oil-producing countries may generate revenue
C No oil-producing countries generate revenue
D All revenue comes from oil
Explanation: We can only conclude that some oil-producing countries may generate revenue from exports.
A Pass rates indicate effectiveness
B Classroom learning provides social benefits
C Students need interaction
D Online learning is convenient
Explanation: If classroom learning provides social benefits that online doesn\'t, pass rates alone don\'t show equal effectiveness.
A P is true
B P is false
C Q is false
D R is false
Explanation: Q∧R→S and S is false means Q∧R is false. But Q and R are both true, so contradiction. This means the initial premise must be wrong, implying P is false.
A All classics engage readers
B Some classics may engage readers
C No classics engage readers
D All engaged readers read classics
Explanation: All classics stand the test of time, which requires relevance, which engages readers.
A Meditation is popular
B Lower readings indicate reduced blood pressure
C Blood pressure affects health
D Meditation is easy
Explanation: If lower readings indicate reduced blood pressure, this strengthens the meditation-health link.
A B is true
B C is true
C B and C are unknown
D Both B and C are true
Explanation: A being true doesn\'t determine B or C. They could be true or false independently.
A All athletes have good character
B Some athletes may have good character
C No athletes have good character
D All people with good character are athletes
Explanation: We can only conclude that some athletes may have good character.
A Slippery slope
B Ad hominem
C Straw man
D Circular reasoning
Explanation: Assuming wage increases lead to business closures and mass unemployment is a slippery slope.
A B is true
B B is unknown
C D is true
D D is unknown
Explanation: A∧B→C and C is true doesn\'t prove B is true; C could be true from other causes. Similarly for D.