The Little Blue Reasoning Book - Brandon Royal [41]
Statement II — All As are Bs — could refer to either diagram (3) or (4).
Statement III — Some As are Bs — could refer to any of diagrams (5), (6), or (7).
Statement IV — Most As are Bs — could refer to either diagram (8) or (9).
STATEMENTS OF LOGICAL EQUIVALENCY
Exhibit 5.5 – Logical Equivalency Statements
TESTING LOGIC-BASED REASONING
Tip #42: Be careful not to reverse the flow of “If … then” statements. “If A, then B” is not the same as “If B, then A.” This is known in logic as the fallacy of affirming the consequent.
Problem 31: Chemist
“If someone is a chemist, he or she is a scientist. Ms. Zubrinski is a scientist. Therefore, she is a chemist.”
Which of the following best explains why the argument above is invalid?
A) Someone cannot be a chemist without being a scientist, so someone cannot be a scientist without being a chemist.
B) Someone cannot be a chemist without being a scientist, but someone can be a scientist without being a chemist.
C) Someone cannot be a scientist without being a chemist, but someone can be a chemist without being a scientist.
D) Someone can be a scientist without being a chemist, and a chemist without being a scientist.
E) Someone can be either a scientist or a chemist, but not one without being the other.
See solution
Tip #43: The statement “If A, then B” leads to the logical inference “If not B, then not A.” This is known in logic as the contrapositive.
Problem 32: Intricate Plots
The ability to create intricate plots is one of the essential gifts of the scriptwriter. Strong plot development ensures that eventual moviegoers will be intellectually and emotionally satisfied by the story. If scriptwriting is to remain a significant art form, its practitioners must continue to craft intricate plots.
The author of the argument above would most probably agree with which one of the following statements?
A) If a script has an intricate plot, it must necessarily be a significant art form.
B) A script without an intricate plot will never become a blockbuster movie.
C) If a script does not have an intricate plot, it will probably not be a significant art form.
D) Scriptwriting is the most likely art form to become a significant art form.
E) A scriptwriter must craft multiple plots within his or her scripts.
See solution
Tip #44: The statement “If A, then B” does not equal “If not A, then not B.” This is known in logic as the fallacy of denying the antecedent.
Problem 33: Campus Pub
“During final exam week, our campus pub sells a lot of beer. But it isn’t final exam week, so our campus pub must not be selling much beer.”
Which of the following is logically most similar to the argument above?
A) When people are happy, they smile, but no one is smiling, so it must be that no one is happy.
B) When people are happy, they smile; our family members are happy, so they must be smiling.
C) When people are happy, they smile, but one can smile and not be happy.
D) When people are happy, they smile, but no one is happy, so no one is smiling.
E) When people are not happy, they do not smile; our family members are smiling, so they must not be unhappy.
See solution
Tip #45: One way to think about an “If … then” statement in the form of “If A, then B” is that just because A leads to B does not mean that C, D, or E could not also lead to B.
Problem 34: Balcony
If your apartment is above the fifth floor, it has a balcony.
The statement above can be logically deduced from which of the following statements?
A) No apartments on the fifth floor have balconies.
B) An apartment does not have a balcony unless the apartment is above the fifth floor.
C) All apartments above the fifth floor have balconies.
D) All balconies are built for apartments above the fifth floor.
E) Balconies are not built for apartments below the fifth floor.
See solution
Tip #46: Necessary conditions are not the same as