A All fish are dangerous
B Some fish may be dangerous
C No fish are dangerous
D All safe creatures are fish
Explanation: We can only conclude that some fish may be dangerous.
A Slippery slope
B Ad hominem
C Straw man
D Circular reasoning
Explanation: Assuming giving trophies leads to no one trying hard is a slippery slope.
A B is true
B B is false
C A is false
D Both A and B are true
Explanation: A is true, so for A∧B→C, if C is false, then A∧B is false, meaning B is false.
A All fruits prevent disease
B Some fruits may prevent disease
C No fruits prevent disease
D All disease preventers are fruits
Explanation: We can only conclude that some fruits may prevent disease.
A Fiction provides diverse perspectives
B Exposure to diversity builds empathy
C Empathy is valuable
D All of the above
Explanation: For the argument to hold, all these assumptions must be true.
A Q is true
B R is true
C Q or R is false
D Both Q and R are true
Explanation: P→Q and P true means Q is true. Q→R means R is true. P∧R→S means if both P and R true, S should be true. S false means either Q or R must be false, contradicting earlier steps.
A All students are innovative
B Some students are not boring
C No students are boring
D All boring people are students
Explanation: Some students are creative, some creative people are innovative, and no innovative person is boring, so some students are not boring.
A Social media connects people
B Self-reported loneliness may have other causes
C Isolation is bad
D Social media is widespread
Explanation: If self-reported loneliness has other causes, social media may not be the cause.
A B is true
B B is false
C A is false
D Both B and C are true
Explanation: A∧B→C and C is false means A∧B is false. Since A is true, B must be false.
A All mammals form groups
B Some mammals may form groups
C No mammals form groups
D All group-formers are mammals
Explanation: We can only conclude that some mammals may form groups.
A Meditation is popular
B Lower anxiety levels indicate reduced anxiety
C Anxiety is harmful
D Studies are reliable
Explanation: If lower anxiety levels indicate reduced anxiety, this strengthens the causal claim.
A D is true
B D is false
C D is unknown
D B is false
Explanation: By transitivity of equivalence, if A↔B↔C↔D and A is true, D is true.
A All books are digital
B Some books may be digital
C No books are digital
D All digital resources are books
Explanation: We can only conclude that some books may be digital.
A Diversity improves performance
B Companies should hire diverse candidates
C Performance matters
D Diversity exists
Explanation: The recommendation to hire diverse candidates is the conclusion.
A Q is true
B R is true
C Q or R is false
D Both Q and R are true
Explanation: P→Q and P true means Q true. P→R and P true means R true. Q∧R→S means if both true, S should be true. S false means contradiction.
A All democracies have good governance
B Some democracies may have good governance
C No democracies have good governance
D All good governance comes from democracies
Explanation: We can only conclude that some democracies may have good governance.
A Clean energy requires infrastructure
B Infrastructure requires workers
C Workers need jobs
D All of the above
Explanation: For the argument to work, all these assumptions must hold.
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: A∧B→C and A true means if B true, C true. A∧C→B means if C true, B true. B∧C→A means if both true, A true (already given). This is consistent.
A All students improve their skills
B Some students improve their skills
C No students improve their skills
D All skilled people are students
Explanation: Since some students are musicians and musicians practice daily to improve, some students improve their skills.
A Borrowing increases spending
B People may save low rates instead of borrowing
C Spending helps the economy
D Interest rates affect borrowing
Explanation: If people save the benefit of low rates rather than borrowing, the economic boost is weakened.