A Q is true
B R is true
C Q and R can\'t both be true
D P is false
Explanation: P→Q and P true means Q true. P→R and P true means R true. Q∧R→S means S should be true, but S is false, creating a contradiction.
A All citrus is used in cooking
B Some citrus may be used in cooking
C No citrus is used in cooking
D All cooking ingredients are citrus
Explanation: We can only conclude that some citrus may be used in cooking.
A Exercise is popular
B Increased muscle mass indicates muscle building
C Muscle is important
D Exercise is healthy
Explanation: If increased muscle mass indicates muscle building, this strengthens the claim.
A A is true
B A is false
C A is unknown
D B is false
Explanation: D→A and D is false doesn\'t tell us about A. The cycle A→B→C→A doesn\'t determine truth values without a starting point.
A All predators succeed
B Some predators may succeed through teamwork
C No predators succeed
D All successful hunters are predators
Explanation: We can only conclude that some predators may succeed through teamwork.
A Online shopping saves time
B Variety is desirable
C Convenience matters to consumers
D All of the above
Explanation: For the argument to hold, all these assumptions must be true.
A P is true
B Q is true
C Both P and Q are false
D P and Q are both true
Explanation: P∧Q→R and R is false means P∧Q is false. Since exactly 2 are true and R is false, P and Q can\'t both be true. So both must be false, but then only 0 would be true. Contradiction.
A All novels require suspense
B Some novels may require suspense
C No novels require suspense
D All suspenseful things are novels
Explanation: We can only conclude that some novels may require suspense.
A Happiness improves productivity
B Home distractions reduce productivity
C Employees prefer home
D Productivity is measurable
Explanation: If home distractions reduce productivity, the happiness benefit may be offset.
A B is true
B C is true
C B and C can\'t both be true
D A is false
Explanation: A→B and A true means B true. A→C and A true means C true. B∧C→D means D should be true, but it\'s false. Contradiction.
A All students excel in sports
B Some students may excel in sports
C No students excel in sports
D All sports excellence comes from students
Explanation: We can only conclude that some students may excel in sports.
A Slippery slope
B Ad hominem
C Straw man
D Circular reasoning
Explanation: Assuming one allowance leads to everything being allowed is a slippery slope.
A P is true
B P is false
C P is unknown
D All of P-S are true
Explanation: T being true doesn\'t prove P is true. The chain could have been triggered by other causes.
A All countries are productive
B Some countries may be more productive
C No countries are productive
D All productive countries have UHC
Explanation: We can only conclude that some countries may be more productive due to UHC.
A Reading is popular
B Vocabulary tests accurately measure vocabulary
C Vocabulary matters
D Tests are standardized
Explanation: If vocabulary tests accurately measure vocabulary, higher scores strengthen the reading-vocabulary link.
A C is true
B C is false
C C is unknown
D A is false
Explanation: A∧C→B and B is false means A∧C is false. Since A is true, C must be false.
A All organic fruits are healthy
B Some organic fruits may be healthy
C No organic fruits are healthy
D All healthy foods are organic
Explanation: We can only conclude that some organic fruits may be healthy.
A Green buildings use efficient materials
B Efficiency saves energy
C Energy savings are valuable
D All of the above
Explanation: For the argument to hold, all these assumptions must be true.
A Contradiction
B B is true
C B is false
D A is false
Explanation: A↔B and A true means B true. B↔C and B true means C true. But C is false, creating a contradiction.
A All students are reliable
B Some students may be reliable
C No students are reliable
D All reliable people are scientists
Explanation: We can only conclude that some students may be reliable scientists.