A Exercise is popular
B Longer life indicates better health
C Health is important
D Studies are reliable
Explanation: If longer life indicates better health, this strengthens the claim that exercise improves health.
A B is true
B B is false
C B is unknown
D Cannot determine
Explanation: If A∧B→C and C is false while A is true, B must be false.
A Shape X is a square
B Shape X might be a square
C Shape X is not a square
D All four-sided shapes are squares
Explanation: Having four sides is necessary but not sufficient for being a square.
A Free speech
B An attempt to silence dissent
C A democratic principle
D A logical argument
Explanation: Prohibiting criticism of government is an attempt to silence dissent.
A P is true
B P is false
C P is unknown
D P is contradictory
Explanation: Q being true doesn\'t prove P is true; P is necessary but not sufficient.
A All countries use euros
B Some countries use euros
C No countries use euros
D All euro-using countries are European
Explanation: Since some countries are in Europe and all European countries use euros, some countries use euros.
A Smoking kills
B We should ban cigarettes
C Cigarettes are bad
D Health matters
Explanation: The recommendation to ban cigarettes is the conclusion supported by the premise.
A B is true
B B is false
C A is false
D Both are true
Explanation: If not both A and B can be true and A is true, B must be false.
A Mr. Smith educates
B All educators are teachers
C Some teachers don\'t educate
D Mr. Smith is not a teacher
Explanation: By syllogism, Mr. Smith educates.
A A valid argument
B An ad hominem attack
C A logical deduction
D A fact
Explanation: Dismissing someone\'s trustworthiness based on their profession is an ad hominem.
A P implies R
B R implies P
C P and R are unrelated
D Q implies P and R
Explanation: Two different things can imply the same thing without implying each other.
A All books are fiction
B Some books are fiction
C No books are fiction
D All fiction is books
Explanation: Since some books are novels and all novels are fiction, some books are fiction.
A Taxes will be raised
B People respond to tax increases
C Leaving is bad
D Taxes are too high
Explanation: The argument assumes that people will leave in response to tax increases.
A B is true
B B is false
C B is unknown
D A is false
Explanation: If A is sufficient for B and A occurs, B must be true.
A Flower X is a rose
B Flower X might be a rose
C Flower X is not a rose
D All things needing water are roses
Explanation: Needing water doesn\'t prove something is a rose; it\'s a necessary but not sufficient condition.
A TV is popular
B Violent people watch more TV
C Other factors cause violence
D TV is entertaining
Explanation: If other factors cause violence, TV may not be the cause.
A P→Q and Q→P
B Only P→Q
C Only Q→P
D Neither P→Q nor Q→P
Explanation: Necessary and sufficient means the implication works both ways.
A All animals are cold-blooded
B Some animals are cold-blooded
C No animals are cold-blooded
D All cold-blooded things are reptiles
Explanation: Since some animals are reptiles and all reptiles are cold-blooded, some animals are cold-blooded.
A A logical argument
B An appeal to popularity
C A democratic principle
D A factual claim
Explanation: Arguing something is good simply because many people support it is an appeal to popularity.
A Q is false
B Q is true
C Both are false
D Both are true
Explanation: If P and Q cover all possibilities and are mutually exclusive, and P is false, Q must be true.