Sets of operation (Checking)

Question

Hello! I just wanted to see if my answer is correct. Would someone please check this..Thanks in advance😀

Universal/Union = { a,b,c,d,e,f,g,h}

A = {a,b,c,d}             A' = {e,f,g,h}

B = {e,f,g,h}.             B' = {a,b,c,d}

C = {a,d,h}                C' = {b,c,e,f,g}

D = {c,d,f,g}              D' = {a,b,e,h}

E = {a,b,c,f,g,h}         E' = {d,e}

Sets:

1.)[ [ [(A' ∩ B')' ∩ (C' ∩ D')']' - [(B-D')'- (A-C')']' ]' - E ]'

2.) [ [ [ [ (A' - B')' -C' ]' - D' ]' - E' ]' ∩ [ ( A' ∪ B')' ∩ (E' ∩ D')' ]' ]' ∩ ( B' '- C' ')' '

3.)[ B' ∩ [ (B' ∪ C')' - ( D' ∩ D) ] ' ]' ∩ [( E ∪ E')' ∩ (C' - E)']'

 

Answer no. 1

 A' ∩ B' = { }

(A' ∩ B')' = {a,b,c,d,e,f,g,h}

 C' ∩ D' = {b,c}

(C' ∩ D')' = {a,d,e,f,g,h}

(A' ∩ B')' ∩ (C' ∩ D')'= {a,c,d,f,g,h}

[(A' ∩ B')' ∩ (C' ∩ D')']' = { b,e}

 

B - D' = {f,g}

(B - D')' = {a,b,c,d,e,h}

A - C' = {a,d}

(A' - C')' = {b,c,e,f,g,h}

 

( B - D')' - (A - C')' = {a,d}

[(B - D')' - (A - C')']' = {b,c,e,f,g,h}

 

[( A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']' = { }

[[ (A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']']' = {a,b,c,d,e,f,g,h}

[[ (A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']']' - E = { e,d}

 

Final Answer:

[ [[ (A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']']' - E ]' = {a,b,c,f,g,h}

 

Answer no. 2 

A' - B' = {e,f,g,h}

(A' - B')' = {a,b,c,d}

 (A' - B')' - C' = {a,d}

[(A' - B')' - C']' = {b,c,e,f,g,h}

[(A' - B')' - C']' - D' = {c,f,g}

[ [(A' - B')' - C']' - D' ]' = {a,b,d,e,h}

[ [(A' - B')' - C']' - D' ]' - E' = {a,b,h}

[ [ [(A' - B')' - C']' - D' ]' - E' ]' = {c,d,e,f,g}

 

A' ∪ B' = {a,b,c,d,e,f,g,h}

(A' ∪ B')' = { }

E' ∩  D' = {e}

(E' ∩ D')' = { a,b,c,d,f,g,h}

(A' ∪ B')' ∩ (E' ∩ D')' = { }

[(A' ∪ B')' ∩ (E' ∩ D')']' = {a,b,c,d,e,f,g,h}

 

[ [ [(A' - B')' - C']' - D' ]' - E' ]' ∩ [(A' ∪ B')' ∩ (E' ∩ D')']' = {c,d,e,f,g}

 

[ [ [ [(A' - B')' - C']' - D' ]' - E' ]' ∩ [(A' ∪ B')' ∩ (E' ∩ D')']' ] ' = {a,b,h}

 

*I cancel out  B' ' - C ' ' 

(B - C)' = {a,b,c,d,h}

[(B - C)']' = {e,f,g}

 

Final Answer:

[ [ [ [(A' - B')' - C']' - D' ]' - E' ]' ∩ [(A' ∪ B')' ∩ (E' ∩ D')']' ] ' ∩ [(B - C)']' = { } 

 

Answer no. 3 

B' ∪ C' = {a,b,c,d,e,f,g}

(B' ∪ C')' = {h}

D' ∩ D = { }

(D' ∩ D)' = {a,b,c,d,e,f,g,h}

 

(B' ∪ C')' - (D' ∩ D)' = { }

[(B' ∪ C')' - (D' ∩ D)']' ={ a,b,c,d,e,f,g,h}

B' ∩ [(B' ∪ C')' - (D' ∩ D)']' = {a,b,c,d}

[ B' ∩ [(B' ∪ C')' - (D' ∩ D)']' ]' ={e,f,g,h}

 

E ∪ E' = {a,b,c,d,e,f,g,h}

(E ∪ E')' = { }

C' - E = {e}

(C' - E)' = {a,b,c,d,f,g,h}

(E ∪ E')' ∩ (C' - E)' = { }

[ (E ∪ E')' ∩ (C' - E)' ] ' = {a,b,c,d,e,f,g,h}

 

Final Answer:

[ B' ∩ [(B' ∪ C')' - (D' ∩ D)']' ]' ∩ [ (E ∪ E')' ∩ (C' - E)' ] ' = { e,f,g,h}

 

Answer 1

Universal = { a,b,c,d,e,f,g,h}

A = {a,b,c,d}             A' = {e,f,g,h}
B = {e,f,g,h}.             B' = {a,b,c,d}

C = {a,d,h}                C' = {b,c,e,f,g}
D = {c,d,f,g}              D' = {a,b,e,h}
E = {a,b,c,f,g,h}         E' = {d,e}

 

1.)[ [ [(A' ∩ B')' ∩ (C' ∩ D')']' - [(B-D')'- (A-C')']' ]' - E ]'

 

A'∩B' = {}

(A' ∩ B')' = {a,b,c,d,e,f,g,h}

C'∩D' = {b,e}      you made a small error here listing {b,c}

(C' ∩ D')' = {a,c,d,f,g,h}

(A' ∩ B')' ∩ (C' ∩ D')' = {a,c,d,f,g,h}

[(A' ∩ B')' ∩ (C' ∩ D')']' = {b,e}

 

(B-D') = {f,g}

(B - D')' = {a,b,c,d,e,h}

A - C' = {a,d}

(A-C')' = {b,c,e,f,g,h}

( B - D')' - (A - C')' = {a,d}

[( B - D')' - (A - C')']' = {b,c,e,f,g,h}

[ [(A' ∩ B')' ∩ (C' ∩ D')']' - [(B-D')'- (A-C')']] = {b,e}-{b,c,e,f,g,h} = {}

[[ (A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']']' = {a,b,c,d,e,f,g,h}

[[ (A' ∩ B')' ∩ (C' ∩ D')']' - [( B - D')' - (A - C')']']' - E = {d,e}

[ [ [(A' ∩ B')' ∩ (C' ∩ D')']' - [(B-D')'- (A-C')']' ]' - E ]' = {a,b,c,f,g,h}

 

Your minor error noted above did not effect the final answer.

 

It is apparent that you are familiar with how to work these so I will

leave you to check the other two.  Have fun and best of luck.