Self-study
University president: Support We will be forced to reduce spending next year if we do not increase our enrollment. ███ ██ ██ ███ ██ ████████ ███ ███████ ██ ███ █████████ ██ ████████ ██ ████ ██████ ███ ████████ ████ █████████████ ███████ ████ █████████ ██ ████ ██ ██████ ██ ████████ ███ ███████████
Summary
The president concludes that the university needs more aggressive marketing to maintain its quality of education. She uses two premises to support this:
1. If enrollment doesn’t increase, the university will have to reduce spending. By the contrapositive, if the university doesn’t reduce spending, its enrollment will need to increase.
2. If the university doesn’t market more aggressively, its enrollment won’t increase. By the contrapositive, if the university increases enrollment, it must have marketed more aggressively.
Missing Connection
The idea of maintaining quality is in the conclusion, but it isn’t in the premises! So the answer choice will need to link “maintain quality” with the premises in one of the following ways:
1. To maintain quality, the university must not reduce spending; or, by the contrapositive, reduced spending would result in a difference in quality
2. To maintain quality, the university must increase enrollment; or, by the contrapositive, if enrollment doesn’t increase, quality will not be maintained.
20.
The conclusion of the university ███████████ ████████ ███ ██ ████████ █████ ██ █████ ███ ██ ███ █████████ ██ ████████
a
The university will ███ ████████ ███ ███████ ██ ███ █████████ ██ ████████ ██ ██ █████████ ███ ███████████
To reach the conclusion by linking “maintain quality” with “increase enrollment,” the link would need to be: “If the university maintains quality, enrollment increases.” Instead, (A) says (by the contrapositive): “if the university maintains quality, enrollment won’t increase.”
b
The university will ███ ████ ██ ██████ ████████ ████ ████ ██ ██ █████████ ███ ███████████
This answer choice says nothing about maintaining education quality, so it cannot provide the missing connection between “maintain quality” and the existing premises. Without that connection, the conclusion can’t be properly drawn!
c
The university will ████████ ███ ██████████ ██ ██ ███████ ███ ████████ ████ █████████████
This answer choice says nothing about maintaining education quality, so it cannot provide the missing connection between “maintain quality” and the existing premises. Without that connection, the conclusion can’t be properly drawn!
d
The university will ███ ████████ ███ ███████ ██ ███ █████████ ██ ████████ ██ ██ ███████ ████████ ████ █████
By the contrapositive, (D) says: “if the university maintains quality, it won’t reduce spending.” As shown below, this premise fits into the conditional chain and allows us to properly draw the president’s conclusion!
e
The university will ███ ████ ██ ██████ ████████ ████ ████ ██ ██ ███████ ███ ████████ ████ █████████████
This answer choice says nothing about maintaining education quality, so it cannot provide the missing connection between “maintain quality” and the existing premises. Without that connection, the conclusion can’t be properly drawn!