Math

3 questions if you can help me.

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)

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  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)?

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