In a survey of a TriDelt chapter with 50 members, 18 were taking mathematics, 37 were taking English, and 7 were taking both. How many were not taking either of these subjects?

draw 2 intersecting circles, label one M and the other E

place 7 in the intersection of both
Now look at the M circle, it should contain 18, but we have already placed 7 in that circle, so put 11 in the open part of circle M
Now look at the E circle, it should contain 37, but we have already placed 7 in that circle, so put 30 in the open part of circle E

now adding these numbers up I get
11 + 7 + 30 = 48

but we surveyed 50 people, so 2 must have been outside our two circles ----> 2 were not taking either of these.

As and equation we could have done:
Number(M or E) = number(M) + number(E) - number (M AND E)
number(M OR E) = 18+37 - 7 = 48

You will probably get questions with 3 circles.
Repeat the same method as above, except you would have an inner intersection of 3 items, start with that.

To find the number of members who were not taking either math or English, we need to subtract the number of members taking both subjects from the total number of members.

We are given that there are 50 members in total and that 7 members are taking both math and English.

Therefore, the number of members not taking either math or English is:

Total members - Members taking both subjects = 50 - 7 = 43

So, there were 43 members who were not taking either mathematics or English.

To solve this problem, we can use the principle of inclusion-exclusion. Let's break it down step by step.

Step 1: Find the total number of members who were taking mathematics, English, or both.
- According to the survey, 18 members were taking mathematics, 37 members were taking English, and 7 members were taking both subjects.
- To find the total number of members taking either mathematics or English, we add the number of members taking mathematics (18) and the number of members taking English (37): 18 + 37 = 55.

Step 2: Determine the number of members who were taking either mathematics or English but not both.
- Since we already calculated that 7 members were taking both mathematics and English, we need to subtract this number from the total number of members taking either mathematics or English: 55 - 7 = 48.

Step 3: Find the number of members who were not taking either mathematics or English.
- To find this number, we subtract the number of members taking either mathematics or English but not both (48) from the total number of members in the chapter (50): 50 - 48 = 2.

Therefore, there were 2 members who were not taking either mathematics or English.