SOLUTION: Let p be Ricky love Lucy and let q be Lucy loves Ricky. Give a verbal translation. a Pv~Q b ~P^~Q c~(P^Q) 2. Construct truth table for the following a Pv~Q b Pv(Q^r) c ~P

In this problem, you are given a universe set of all 100 students
and its three basic subsets

    E of 60 students learning English
    M of 40 students learning Math
    C of 50 students learning Chemistry.

You are also given in-pair intersections of these three subsets

    EM of 30 students learning English and Math
    EC of 35 students learning English and Chemistry
    MC of 35 students learning Math and Chemistry

You are also given the triple intersection EMC of 25 students learning all three subjects.



(a)  how many students were taking mathematics, but neither English nor chemistry ?

     To answer this question, we subtract the quantities EM and MC from M, first.

     But doing it, we subtract the amount in the triple intersection EMC twice.
     Therefore, to compensate it, we add EMC at the end, so out formula is

        n(M_only) = n(M) - n(EM) - n(MC) + n(EMC) = 40 - 30 - 35 + 25 = 0.    ANSWER



(b)  how many were taking mathematics and chemistry but not English ?

     To answer this question, we take the quantity n(MC) and subtract quantity n(EMC) from it

        n(MC_only) = n(MC) - n(MCE) = 35 - 25 = 10.    ANSWER



(c)  how many were taking English and chemistry but not mathematics ?

     This question is very similar to (b), and the answer to it is very similar to (b), too.


     To answer this question, we take the quantity n(EC) and subtract quantity n(EMC) from it

        n(EC_only) = n(EC) - n(MCE) = 35 - 25 = 10.    ANSWER