Question

Спростити вираз 1.(A ∪ U ∩ (B̄ ∩ B)) ∪ AĀ 2.(A ∪ B ∩ C) ∩ (A ∪ B̄ ) 3.((A ∪ B)\(AA ∪ B̄ )) ∪ B 4.(A\B)\(B \C)\A 5.(A ∪ B̄ ∪ B̄ ∩ C ∩ A ∪ B̄ ∪ C̄ ) ∩ (A ∩ (B\A))

Answer 1

это на каком языке Я не понимаю?

Answer 2

1. (A ∪ U ∩ (B̄ ∩ B)) ∪ AĀ

Let's simplify the expression step by step:

1. Ā ∩ B: The complement of A (∀U - A) intersected with B (∀U - B) gives an empty set (∅) because the complement of a set and its intersection with another set would result in an empty set.

2. U ∩ (B̄ ∩ B): The complement of B (∀U - B) intersected with B gives an empty set as well (∅) for the same reason mentioned in step 1.

3. A ∪ ∅: The union of A with an empty set (∅) is just A.

4. A ∪ AĀ: The union of a set with its complement (∀U - A) is the universal set U.

Therefore, the simplified expression is U.

2. (A ∪ B ∩ C) ∩ (A ∪ B̄)

Let's simplify the expression step by step:

1. B ∩ C: The intersection of B and C gives a set (B ∩ C).

2. A ∪ (B ∩ C): The union of A with (B ∩ C) gives a set (A ∪ (B ∩ C)).

3. B̄: The complement of B (∀U - B) is a set.

4. A ∪ B̄: The union of A with B̄ (∀U - B) gives a set (A ∪ B̄).

5. (A ∪ (B ∩ C)) ∩ (A ∪ B̄): The intersection of (A ∪ (B ∩ C)) and (A ∪ B̄) gives the final set.

The expression is simplified as (A ∪ (B ∩ C)) ∩ (A ∪ B̄).

3. ((A ∪ B)(AA ∪ B̄ )) ∪ B

Let's simplify the expression step by step:

1. AA: The complement of A (∀U - A) is a set.

2. AA ∪ B̄: The union of AA and the complement of B (∀U - B) gives a set (AA ∪ B̄).

3. (A ∪ B)(AA ∪ B̄): The difference between the union of A and B and (AA ∪ B̄) gives a set ((A ∪ B)(AA ∪ B̄)).

4. ((A ∪ B)(AA ∪ B̄)) ∪ B: The union of ((A ∪ B)(AA ∪ B̄)) and B gives the final set.

The expression is simplified as ((A ∪ B)(AA ∪ B̄)) ∪ B.

4. (A\B)(B \C)\A

Let's simplify the expression step by step:

1. A\B: The set difference between A and B gives a set (A\B).

2. B \ C: The set difference between B and C gives a set (B \ C).

3. (A\B)(B \ C): The set difference between (A\B) and (B \ C) gives a set ((A\B)(B \ C)).

4. (A\B)(B \ C)\A: The set difference between ((A\B)(B \ C)) and A gives the final set.

The expression is simplified as (A\B)(B \ C)\A