Word Problems/Mathematics

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Question
E= {positive integers less than 100}
M2= {multiples of 2 less than 100}
M3= {multiples of 3 less than 100}
M4,M5 etc. are defined in a similar matter.

a) List all the elements of the set M10 ∩ M6
b) Write which of the M sets is the same as:
i) M3 ∩ M6
ii) M4 ∩ M6

c) Draw a venn diagram showing the relationship between E M6 M9 and M12.

(Okay, i know what a venn diagram is, but help me with how to set up the information please?)

Thanks you for your time!

Answer
This response is all about the prime factors.

a) M10 ∩ M6 is the set of all number between 1 and 100 that are divisible by 6 and 10.
Since the prime factors of 10 are 2 and 5 and the prime factors of 6 are 2 and 3,
it would be all numbers between 1 and 100 with prime factors 2,  3, and 5.
Since 2*3*5 = 30, this means it would be 30, 60, and 90.
Adding 30 again gives 120, and that is outside the range.

bi) Since 6 = 2*3, all of the elements in M6 are in M3, so the answer is M3.
bii) Sinc 4 = 2*2 and 6 = 2*3, the number with all of these factors is 2*2*3 = 12.
That would make it the set M12.

c) Since 6 is 2*3, 9 is 3*3, and 12 is 2*2*3, M12 is inside of M6.
M9 would be a shape that had some elements in both sets and some in neither.

This means M12 could be a circle of radius 1, M6 would then be a circle of radius 2 with the same center, and M12 would be an oval with a center at a point on the right edge of M12 that intersected M12, M6 alone, and included area that was outside of both regions.

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