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(5) Simplify the following sets:

The letter "c" indicates that it refers to the complement.


[Exercise 36] (A ∩ B) ∩ (A ∩ Bc)

 

(A ∩ B) ∩ (A ∩Bc)

(B∩A) ∩ (A ∩ Bc)

B∩ (A ∩ A) ∩ Bc

(A ∩ A) ∩ B ∩ Bc

(A ∩ A) ∩ (B ∩ Bc)

A ∩ Ø

Ø


2. [Exercise 37] (Ac ∩ B)c ∪ (B ∪ Ac)c ∪ A
3. [Exercise 38] (A ∩ Bc) ∩ (Ac ∩ B)

 

(A ∩ Bc) ∩ (Ac ∩ B)

A ∩ (Bc ∩ B) ∩ Ac

(Bc ∩ B) ∩ A ∩ Ac

(Bc ∩ B) ∩ (A ∩ Ac)

Ø∩Ø

Ø


4. [Exercise 39] (A ∪ A) - (A∩ B)


5. [Exercise 40] (A ∩ B) ∪ (Bc ∪ Ac)

[(A ∩ B) ∪ Bc] ∪ [(A∪ B) ∩ Ac]

(Bc ∪ B) ∪ (Bc ∪ A) ∪ (Ac ∩ B) ∪ (Ac ∩ A)

U ∪ (Bc ∪ A) ∪ (Ac ∩ B) ∪ Ø

U