1. In a survey of a TriDelta chapter with 46 members, 13 were taking mathematics, 33 were taking English, and 6 were taking both. How many were not taking either of these subjects?

No One was Not taking any of these,Because 33+13=46

N(Math OR English) = N(Math) + N(English) - n(Math AND English)

= 13 + 33 - 6
= 40

So 40 took either Math or English, then
6 took neither of these subjects

You can also do this with Venn diagrams

Subtract 6 from 13 and from 33.

Then add 6 back just once.
7 + 27 + 6 = 40 students are taking either one or both of the subjects.

So 46 - 40 = 6 students are taking neither of the subjects.

To find out how many members were not taking either mathematics or English, we need to consider the total number of members and subtract the number of members taking either mathematics or English or both.

Let's break down the information we have:

- Total number of members: 46
- Number of members taking mathematics: 13
- Number of members taking English: 33
- Number of members taking both: 6

To find the number of members not taking either subject, we can use the principle of inclusion-exclusion.

First, we add the number of members taking mathematics and the number of members taking English:
13 + 33 = 46

But by doing this, we have double-counted those 6 members who are taking both subjects. So, we need to subtract the number of members taking both:
46 - 6 = 40

Therefore, 40 members are taking either mathematics or English or both. To find the number of members not taking either subject, we subtract this number from the total number of members:
46 - 40 = 6

Therefore, there are 6 members who are not taking either mathematics or English.