Question

Suppose P and Q are equivalent sets and n(P)=17.
What is the maximum number of elements in P u Q? What is the minimum?
What is the maximum number of elements in P n Q? What is the minimum?

Any help is appreciated! Thanks!

Answer 1

I think maximum of n (P or Q) = 34
minimum is 0 (the case they are not overlap at all. I mean they are separated)
the max of n(P and Q) = 17. the min =0.

Answer 2

Yes. For example if

P = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
and
Q = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r}

then n(PuQ) = 34. But if P = Q then n(PnQ) = 17

Answer 3

Thanks a lot, for both "works" and check my work