SOLUTION: a.If A has six elements and B has eight elements, how many elements are in A x B? b. If A has g elements and B has h elements, how many elements are in A x B? c. If A has g eleme

Question 974543: a.If A has six elements and B has eight elements, how many elements are in A x B?
b. If A has g elements and B has h elements, how many elements are in A x B?
c. If A has g elements, B has h elements, and C has k elements, how many elements are in (A x B) x C?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

There are 6*8 = 48 elements in set A x B

Rule: If there are m elements in A, n elements in B, then there are m*n elements in A x B. Draw out a table to see why this works.

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b)

We use the same rule applied in part a). There are g*h elements in A x B. If we knew the numeric values of g and h, we can get a single numeric answer like we did in part a).

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c)

There are g*h*k elements in (A x B) x C

Think of A x B as one set. Call it Q. In other words, let Q = A x B

So (A x B) x C turns into Q x C and we'll use the rules applied in part a) and part b). Q is going to have g*h elements in it. So Q x C has (g*h)*k = g*h*k elements in it.
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