Let x = {1, 2} and let y = {3, 4}. define f : p(x) × p(y ) ? p(x ? y ) by f(a, b) = a ? b.
(a) find (a, b) ? p(x) × p(y ) such that f(a, b) = {2, 3}.
(b) find (a, b) ? p(x) × p(y ) such that f(a, b) = {2, 3, 4}.
(c) given c ? p(x ? y ), find (a, b) ? p(x) × p(y ) such that f(a, b) = c.

Aprobability experiment is conducted in which the sample space of the experiment is s={7,8,9,10,11,12,13,14,15,16,17,18}, event f={7,8,9,10,11,12}, and event g={11,12,13,14}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.