SOLUTION: A. Given U = (x | x is a letter in the english alphabet) A = (a, b, c, d, e) B = (a, f, g, h) C = (a, c, h, i) Find the following sets. 1. (B ∩ C) ∩ A' 2. C U Ø 3. (A

I'll just do 2 of them.

U = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}

1.  (B ∩ C) ∩ A'
Substitute
({a,f,g,h} ∩ {a,c,h,i}) ∩ {a,f,g}'

We do this part first {a,f,g,h} ∩ {a,c,h,i}. Intersection means to take ONLY
the elements in common, we get {a,h} to substitute for what's in the first
parentheses and get:

({a,h}) ∩ {a,f,g}' 

Next we do {a,f,g}'.  The ' means to take the complement, so we take all the
elements in U except a,f,g which is 
                    {b,c,d,e,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}

So now we have:

({a,h}) ∩ {b,c,d,e,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}

Intersection means to take ONLY the elements in common, and there is only one
element in common and that is h.

answer: {h}

-------------------------------------


3. (A ∩ B) U (A ∩ C)

({a,b,c,d,e}  ∩ {a,f,g,h}) U ({a,b,c,d,e} ∩ {a,c,h,i})

First we do ({a,b,c,d,e}  ∩ {a,f,g,h}). Intersection means to take ONLY the
elements in common, and and there is only one element in common and that is a.
So we now have

{a} U ({a,b,c,d,e} ∩ {a,c,h,i})

Next, we do ({a,b,c,d,e}  ∩ {a,c,h,i}). Intersection means to take ONLY the
elements in common, and and there is only two elements in common and they are
a and c.  So we substitute {a,c}, and have:

{a} U {a,c} Union means to take ALL the elements in both sets whether in common

or not.  We list "a" only once,

So the answer is:

{a,c}

Edwin