SOLUTION: Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where:? A={2,5,6,7,14,18,20} B={1,3,4,5,7,8,9,10,11,17,20} C={1,2,3,4,6,10,12,14,

Algebra ->  Subset -> SOLUTION: Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where:? A={2,5,6,7,14,18,20} B={1,3,4,5,7,8,9,10,11,17,20} C={1,2,3,4,6,10,12,14,      Log On


   

Question 1047210: Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where:?
A={2,5,6,7,14,18,20}
B={1,3,4,5,7,8,9,10,11,17,20}
C={1,2,3,4,6,10,12,14,15,16,17,20}

Find the number of elements in the set (A∩C) ∩ B n[(A∩C)∩Bc]
Found 2 solutions by stanbon, AnlytcPhil:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where:? {
A={2,5,6,7,14,18,20}
B={1,3,4,5,7,8,9,10,11,17,20}
C={1,2,3,4,6,10,12,14,15,16,17,20}
Find the number of elements in the set (A∩C) ∩ B n[(A∩C)∩Bc]
----
(A and C) = n{2,6,14,20}
-----
(A and C) and B = {20}
B' = {2,6,12,13,14,15,16,18,19}
(A and C) and B' = {-}
====
Ans:: Zero
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Cheers,
Stan H.
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Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!


Find the number of elements in the set

 (A∩C) ∩ B ∩ [(A∩C) ∩ Bc]

First we find 

A∩C = {2,5,6,7,14,18,20} ∩ {1,2,3,4,6,10,12,14,15,16,17,20} 

Take the elements in common to A and C:

A∩C = {2,6,14,20}

We find Bc = B={1,3,4,5,7,8,9,10,11,17,20}c

That's the set of all elements in the universal set S
which are not elements of B

S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

So 

Bc = {2,6,12,13,14,15,16,18,19} 

We find (A∩C) ∩ B

(A∩C) ∩ B = {2,6,14,20} ∩ {1,3,4,5,7,8,9,10,11,17,20}

By taking the elements in common:

(A∩C) ∩ B = {20}  (There's only one!)

Next we find

[(A∩C) ∩ Bc] = {2,6,14,20} ∩ {2,6,12,13,14,15,16,18,19}

Taking the elements in common:

[(A∩C) ∩ Bc] = {2,6,14} 

So

 (A∩C) ∩ B ∩ [(A∩C) ∩ Bc]

      {20} ∩ {2,6,14}

There are no elements in common, so the answer 
is the empty set:

Answer = n(Ø) which is 0. 

Edwin