Self-study
Support People who have never been asked to do more than they can easily do are people who never do all they can. ████ ██ ███████ ███ ███ ███████ ███ ████ ███ ████ ██ ██ ███████ ██ ██████ ██ █████████ ██ ███ ███ ████ ██████ ███ ██ ██ ████ ████ ████ █████ ██ ███ ███████
Method of Reasoning
The argument presents a conditional relationship (if you’ve never been asked to do more than you can easily do, you never do all you can), then gives an example of someone who confirms the necessary condition (Alex, who hasn’t done all that he can), and then moves to a conclusion (no one has pushed Alex to do more than what comes to him easily).
Identify and Describe Flaw
This is a cookie-cutter confusing necessary and sufficient conditions flaw. The argument says that Alex confirms the necessary condition (he hasn’t done all that he can) and then erroneously infers the sufficient condition (he’s never been asked to do more than he can easily do). Confirming the necessary condition in a relationship tells us nothing about the sufficient condition.
17.
The flawed reasoning in which ███ ██ ███ █████████ ██ ████ ███████ ██ ███ ██████ █████████ ██ ███ ████████ ██████
a
Anybody who has █ ███ █████ ███ ████ █████ ██ ██████████████ ███ ██████ ███ ████████████ ████ ███ █████ ███ ████ █████ ██ ██████████████ ████ ██ ███ ██████ ████████ ████ ██████ ███ █ ████
The argument presents a conditional relationship (if you have a dog, you know the true value of companionship), gives an example of someone who confirms the necessary condition (Alicia, who knows the true value of companionship), and then moves to a conclusion (Alicia has a dog). This commits the same confusing necessary and sufficient conditions flaw as the stimulus. Confirming the necessary condition (that you know the true value of companionship) tells us nothing about the sufficient condition (that you own a dog).
b
Anyone who discovers █████████ ███ ██ ███████ ███ ███ ████████ ███ ███ ████████ █████████ ██ █ ████████ ████ ███ ██████ █████ ██████████ █████████ ████ ██████████ ████ ███ █████ ████████ ███ ███ ████████ █████████ ██ █ ████████
Wrong flaw. This denies the sufficient condition (Fran has never discovered something new) and, as a result, denies the necessary condition (Fran hasn’t explored all the possible solutions to a problem). Denying the sufficient condition in a conditional relationship tells you nothing about the necessary condition. The stimulus, meanwhile, didn’t deny its sufficient condition.
c
Any person who ████ ███ ████ ██████████ ██████████ ██ █ ██████ ███ ████ ███ ██████████ ██████████ ██ ██ ███ ████ ████ ██ █ ██████ ███ ████████████ ██████████ ███ ████ ██ ████ ██ █ ██████ ███ █████ ██████████ ███████████
No flaw. This denies the necessary condition (Jill is a person who accomplishes everything) and, as a result, denies the sufficient condition (Jill is a person who faces sufficient challenges). This is a valid use of the contrapositive.
d
By definition, a ███████ ██ ███ ██████ █████ ██████ ███████ ██ ████████ ██████ ████ ██████ ████████ ██ ███ ██████████ ██ █████████ █ ██████ █████ ██████ ███████ ██ █ █████ ██████ ██ ████████ ██████ ██ ████ ██████ ████████ ██ ███ ██████████ ████ ██ █ ████████
No flaw. Any closed plane figure bounded by straight lines is a polygon. The figure on the board is a closed plane figure bounded by straight lines, so it’s a polygon.
e
People who have █████ ████ █████████ ████ ████ ██████ ██████ ██ ████ ████ ██ ███ █████ ███████ █████ ████████ ███████ ███ ██ ███ █████ ███████ ████████ ██████ ████ ██ ██ █████████ ██ ███ ██████ ██ █████ ██ ███ ████ █████ ████ ████ █████████
Wrong flaw. (E) errs because it triggers neither the sufficient (people who haven’t lost something they can’t afford to lose) nor the necessary (will be lax about keeping their property secure) conditions, yet still tries to draw a conclusion. Jon being lax about keeping property secure when it’s something he can afford to lose isn’t the same as the necessary condition, and Jon having never lost anything isn’t the same as the sufficient condition. The stimulus, meanwhile, doesn’t fail to trigger its necessary condition.