How would this be translated?
Tulane increasing enrollment is a necessary condition for Duke’s reducing class size if and only if Fordham’s raising tuition is a sufficient condition for Georgetown’s expanding course offerings
How would this be translated?
Let
p = "Tulane increases enrollment"
q = "Duke’s reduces class size"
r = "Fordham’s raises tuition"
s = "Georgetown expands course offerings"
Then the original statement becomes:
p is a necessary condition for q if and only if
r is a sufficient condition for s.
Put in parentheses around the parts:
(p is a necessary condition for q) if and only if
(r is a sufficient condition for s)
Now use these rules
X is a necessary condition for Y ------ Y ® X
X if and only if Y -------------------- X « Y
X is a sufficient condition for Y ----- X ®
(p is a necessary condition for q) if and only if
(r is a sufficient condition for s)
(q ® p) « (r ® s)
That's the final translation.
Note:
A sufficient condition always goes on the LEFT of ®
A necessary condition always goes on the RIGHT of ®
SUFFICIENT ® NECESSARY
Edwin