# A and B are subsets of U, such that A= multiples of B, B= factors of 24 Write down n(A intersects B)

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A and B are given as subsets of U. A is defined as multiples of B, and B is factors of 24. We are asked to find `n(A nn B) ` which is the number of elements in the intersection of A and B.

Assuming that U is the set of positive integers:

B is a finite set: B={1,2,3,4,6,8,12,24}

A is an infinite set: `A={a| a=kb, k in ZZ, b in B} ` (A is the set of elements "a" such that a is a multiple of some "b", an element of B.)

Thus each `a in A ` is a positive integral multiple of 1,2,3,4,6,8,12, or 24. Since every integer is a multiple of 1, A is the set of Natural Numbers or `A=NN ` (With the natural numbers here defined as not including zero.)

Therefore the intersection is every item that belongs to both sets: `A nn B={1,2,3,4,6,8,12,24} `

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`n(A nn B)=8 `

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Note that if U is some other set of numbers the answer would be different. However, when using the term "factors" it is generally assumed to mean positive integral factors.

`A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}`

`B = {1, 2, 3, 4, 6, 8, 12, 24}`

`AnnB={1,2,3,4,6,8,12,24}`

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A and B are subsets of U, such that A= multiples of B, B= factors of 24

Write down n(A intersects B)

B contains the elements: (1, 2 , 3 , 4, 6 , 8, 12, 24, )

A contains the elements: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10,...) Since every number is a multiple of 1.

We want the intersection of A and B which means to find the elements that are common to both so:

A intersect B contains the elements: (1, 2, 3, 4, 6, 8, 12, 24, )