3 questions if you can help me.

Question

1. Calculate the number of subsets and the number of proper subsets for the set.

{x|x is a day of the week}

2. Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.

(A n B)u(A n C)

Answer 1

1. the answer is the "power set", i.e. the set of all possible subsets of the given set. The cardinality of the power set of A is equal to 2^(|A|).
For example:
A={1,2}
power set of A ={∅,1,2,{1,2}}
with 4 elements = 2^2.
so if {x|x is a day of the week},
then
n=|x|=7, and the power set of x has 2^7 members.
The number of proper subset is 1 less than 2^n.

2.
A∩B={q,s,y}
A∩C={w,y}
Can you find (A∩B)∪(A∩C)?