In a survey of a TriDelt chapter with 50 members, 21 were taking mathematics, 32 were taking English, and 6 were taking both. How many were not taking either of these subjects?
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To find the number of members who were not taking either mathematics or English, we first need to determine the number of members taking either mathematics or English.
We can do this using the principle of inclusion-exclusion. According to this principle, the total number of members taking either mathematics or English can be calculated by adding the number of members taking mathematics, the number of members taking English, and then subtracting the number of members taking both subjects (to avoid double counting).
Let's break down the information given:
- Number of members taking mathematics (M): 21
- Number of members taking English (E): 32
- Number of members taking both mathematics and English (M ∩ E): 6
To find the number of members taking either mathematics or English (M ∪ E), we can use the following formula:
M ∪ E = M + E - (M ∩ E)
Substituting the given values:
M ∪ E = 21 + 32 - 6
M ∪ E = 47
Now that we know the number of members taking either mathematics or English (M ∪ E), we can find the number of members not taking either subject by subtracting this number from the total number of members in the TriDelt chapter.
Total number of members in the TriDelt chapter = 50
Number of members not taking either mathematics or English = Total number of members - (M ∪ E)
Number of members not taking either mathematics or English = 50 - 47
Number of members not taking either mathematics or English = 3
Therefore, there were 3 members who were not taking either mathematics or English in the TriDelt chapter.