Help with a math problem (set theory)
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Help with a math problem (set theory)

[From: ] [author: ] [Date: 13-08-18] [Hit: ]
15, ...........
Set A contains all the numbers from 10-100
Set B contains all multiples of 3
Set C contains all squares of numbers,

find x if x=(A ∩ B)-C
(How many numbers are in both A and B but not C?)

I would like it if you also explained how to solve this problem.

-
A = {10, 11, 12, 13, 14, 15, .............., 98, 99, 100 }
B = { 3, 6, 9, 12, 15, 18, 21, 24, ......., 93, 96, 99......}
C = { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, .....}

Now find = (A ∩ B) = {12, 15, 18, 21, .....99}, which all factors of 3 which are > 9 and < 100,
This set will have total 30 elements, as 33*3 = 99 , and we excluded first three, 3, 6, 9,
Now find
x = (A ∩ B) - C
x = {12, 15, 18, 21, ....81, 84, 87, 90, 93, 96, 99} - { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, .....}
x = {12, 15, 18, 21, .....78, 84, 87, 90, 93, 96, 99}

Only one number is common in (A ∩ B) and C, which is 81 factor of three and square of 9
x = factor of 3, which is more than 9, and less than 100, and x is not equal to 81,
there will be Total 29 such numbers in set (A ∩ B) - C

Hope this helped

Vick
1
keywords: set,problem,theory,Help,with,math,Help with a math problem (set theory)
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