Posted by **Roger** on Thursday, June 9, 2011 at 11:59am.

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)

- Math -
**MathMate**, Thursday, June 9, 2011 at 12:21pm
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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