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 

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