Suppose that Larry is taking a class taught by Dr. Evlebank. The course is partly assessed by multiple choice, and the content of the course can be reduced to a few hundred logical propositions of the form "if ??, then ??" or "If ??, then not ??". A concrete example might be: "If demand is downward sloping and supply shifts to the right, then quantity demanded will rise", but we don't need to pin this down to specifics. Multiple choice questions based on these propositions can comprise one, two, three or four propositions compounded together. For example:

Now let's suppose that Larry is lazy, but not crazy: he will study just as much as he needs to in order that he can expect to get a 50% in Dr. Evlebank's course so that he can progress with his degree (but Larry won't learn any more than that he's lazy, remember). What proportion of the course material does Larry need to learn if all of the multiple choice questions are... a) ...in the form of Qul (one proposition per question)? b) ...in the form of Qu2 (two propositions per question)? c) ...in the form of Qu3 (three propositions per question)? (1) ...in the form of Qu4 (four propositions per question)? Qu2. Consider the following propositions: i. ii. A) B) C) D) if A1, then 31 if A1, then not B2 i. is true, ii. is true i. is true, ii. is false i. is false, ii. is true i. is false, ii. is false Qu3. Consider the following propositions: i. ii. iii. if A1, then 31 if A1, then not B2 if A1, then not 33 _I _I _I _I _I _I _I _I . is true, . is true, . is true, . is true, . is false, . is false, . is false, . is false, ii. ii. ii. ii. ii. ii. ii. ii. is true, is true, is false, is false, is true, is true, is false, is false, iii. iii. iii. iii. iii. iii. iii. iii. is true is false is true is false is true is false is true is false Qu1. Consider the following proposition: if A1, then 31 A) The statement is true B) The statement is false Qu4. Consider the following propositions: ii. iii. iv. ifAl, then B1 if A1, then not B2 if A1, then not B3 if A2, then B4 -- hi -- . is true, . is true, . is true, . is true, . is true, . is true, . is true, . is true, . is false, . is false, . is false, . is false, . is false, . is false, . is false, . is false, ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. is true, is true, is true, is true, is false, is false, is false, is false, is true, is true, is true, is true, is false, is false, is false, is false, iii. iii. iii. iii. ii]. iii. iii. iii. iii. iii. iii. ii]. iii. iii. iii. iii. is true, is true, is false, is false, is true, is true, is false, is false, is true, is true, is false, is false, is true, is true, is false, is false, iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. iv. is true is false is true is false is true is false is true is false is true is false is true is false is true is false is true is false