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In a Certain Discrete Math Class, Three Quizzes Were Given #1\# 1

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Essay

In a certain discrete math class, three quizzes were given. Out of the 30 students in the class: 15 scored 12 or above on quiz #1,
12 scored 12 or above on quiz #2,
18 scored 12 or above on quiz #3,
7 scored 12 or above on quizzes #1\# 1 and #2\# 2 ,
11 scored 12 or above on quizzes #1\# 1 and #3\# 3 ,
8 scored 12 or above on quizzes #2 and #3,
4 scored 12 or above on quizzes #1\# 1 , #2, and #3.
(a) How many scored 12 or above on at least one quiz?
(b) How many scored 12 or above on quizzes 1 and 2 but not 3?

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Definitions:

Joseph Wolpe

A psychiatrist who significantly contributed to the development of behavioral therapy through techniques like systematic desensitization.

Conditioning

The process of learning associations between environmental stimuli and behavioral responses, often used to explain behavior modification.

Pavlov

Refers to Ivan Pavlov, a Russian physiologist best known for his discovery of classical conditioning, where he demonstrated how reflexes could be conditioned or learned through association.

Behavior Therapy

A type of therapy that focuses on changing undesirable behaviors through reinforcement, punishment, and other learning principles.

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