Answer: M ∩ P' = {6, 9, 12}
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Step-by-step explanation
I'll refer to ξ as E to make things more simple.
E = set of everything = universal set = sample space
E = {3, 5, 6, 9, 10, 12, 15, 20, 25}
M = {6, 9, 12, 15}
P = {multiples of 5} = {5, 10, 15, 20, 25, 30, 35, ...}
P' = opposite or complement of set P
P' = non-multiples of 5 found in set E
P' = {3, 6, 9, 12}
To form set P' we start with writing down set E, then erase any multiple of 5. You'll erase 5, 10, 15, 20, and 25. This is why we ended up with 3,6,9,12 in set P'.
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To find what is inside set M ∩ P', we look at what is common to both set M and set P'
Let's put the sets side by side for easy comparison
M = {6, 9, 12, 15}
P' = {3, 6, 9, 12}
The items in bold represent what is common to both sets.
Therefore M ∩ P' = {6, 9, 12}
The Venn diagram is shown below. Notice this region is marked in blue. It's the region inside circle M but outside circle P. You can think of the intersection symbol representing the term "and".