Consider the Statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$

question 1

Essay

Consider the statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$
Complete the proof begun below in which the given statement is derived algebraically from
the properties listed in Theorem 6.2.2. Be sure to give a reason for every step that exactly justifies what was done in the step: Proof:
Let $A$ and $B$ be any sets. Then the left-hand side of the equation to be shown is

which is the right-hand side of the equation to be shown. [Hence the given statement is true.]
(The number of lines in the outline shown above works for one version of a proof. If you write
a proof using more or fewer lines, be sure to follow the given format, supplying a reason for
every step that exactly justifies what was done in the step.)

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Definitions:

Negative Symptoms

In psychiatry, refers to the absence or diminution of normal psychological capabilities, such as motivation or emotional expression, especially in schizophrenia.

Absences

Instances of not being present where one is expected, often noted in contexts like employment or school attendance.

Psychotic Disorder

A mental health condition characterized by a disconnection from reality, which might include hallucinations, delusions, and impaired thought processes.

Schizophrenia

A long-term mental disorder involving a breakdown in the relation between thought, emotion, and behavior, leading to faulty perception and inappropriate actions and feelings.