1500 college freshmen were interviewed regarding what subject to will be enrolling for the second se

Anika Klein

Anika Klein

Answered question

2022-01-30

1500 college freshmen were interviewed regarding what subject to will be enrolling for the second semester. It was found out that 850 students will be enrolling in Discrete Math while 700 are willing to enroll in Programming. It was also noted that 500 will be enrolled in Discrete Math and Programming.
You may use Venn diagram to analyze the problem.
How many students will confirm in NEITHER for Discrete Math NOR Programming?

Answer & Explanation

ocretz56

ocretz56

Beginner2022-01-31Added 16 answers

Step 1
For any two sets, A, B, It is known that:
bf|AB|=|A|+|B||AB|
bf|A|=|E||A|
Where E is the universal set and bf|A| indicates the cardinality of A.
Step 2
The number of people that were interviewed was 1500. Hence, bf|E|=1500.
Let the set D represents the set of people enrolling in the subject DM. Hence, bf|D|=850.
Let the set P represents the set of people enrolling in the subject P. Hence, bf|P|=700.
The set bfDP represents the set of people enrolling in both subjects. Hence, bfDP=500..
The set bfDP represents the set of people enrolling in either of the subjects. Calculate bf|DP| as follows.
|DP|=|P||DP|
bf=850+700500
bf=1550500  bf=1050
Hence, the number of people willing to enroll in either of the subjects is 1050.
Step 3
The set bf(DB) represents the set of people enrolling in neither of the subjects. Calculate bf|(DB)| as follows.
bf|(DB)|=|E||DB|
bf=15001050
bf=450
Hence, the number of people willing to enroll in neither of the subjects is bf450.

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