Maths question t1.PLS HELP ME!?

Question

E is the universal set & sets P & Q are subsets.It is given that n(E)=60 & n(P)=n(Q)=15.Find

(a) the maximum number of elements in (PuQ)'

(b) the minimum number of elements in (PuQ)'

ANS:(a) 45

(b) 30

Answer 1

Well, if you wanted to know why....

All you need to do is first competely overlap p and q to find the minimum PuQ and separate p and q to find maximum PuQ and then subtract it from E. So it goes (PuQ)'=60-15 for maximum and 60-30 for minimum...

Answer 2

You have the formula

n(P U Q) = n(P) + n(Q) - n(P intersect Q)

The max number of elements in P intersect Q is 15

(This happens if P =Q).

So using this

n(P U Q) = 15 + 15 - 15 = 30 - 15 = 15.

Now you can find the  number of elements in the complement of P U Q like this

n(P U Q)' = n (Universal set ) - n(P U Q) .

Since E is the universal set and n(E) = 60 we do this

n(P U Q)' = n(E) - n(P U Q) = 60 - 15 = 45.

Problem B is similar

First think of what the mininum number of elements in the

set P intersect Q. Then you can use similar Set identities.

Answer 3

Where you write (PuQ)', I write complement of PuQ.  My Set Theory is from a long time ago and I'm not 100% sure that the terminology hasn't changed

1) Maximum

If the sets P & Q are identical then PuQ has 15 elements and its complement has the remaining 45 elements from E.

2) Minimum

If the sets P & Q do not intersect one another, the PuQ has 30 elements and its complement has the remaining 30 elements from E.

I'd show you with a Venn Diagram (drawing) but I can't do that in Yahoo Answers.