SOLUTION: 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 conditi

Algebra ->  Conjunction -> SOLUTION: 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 conditi      Log On


   

Question 114116: 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.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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