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g100num [7]
3 years ago
12

Which subset of the real numbers contains the square root of 50

Mathematics
1 answer:
Pie3 years ago
8 0
There are an infinite number of such subsets. One of them is the set of real numbers in the interval (7, 8). Perhaps you're thinking "irrational" numbers, as opposed to "integers" or "rational" numbers.
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a) A∩B this symbol means the intersection between A and B, in the Venn diagram, is represented by the crossing between the two circles.

According to the diagram there are 9 cardinalities shared by both circles so

A∩B= 9

b) A∪B is the union between both events, it means that you are looking for the cardinalities that are included in A or B but not both, symbolically this is:

A∪B= A + B - A∩B

The total cardinalities included in A are 5 + 9= 14

The total cardinalities included in B are 6 + 9= 15

Note that the elements in the intersection are included in both circles, meaning that they will be counted twice, this is why you have to subtract it.

A∪B= A + B - A∩B= 14 + 15 - 9= 20

c) A∩B'

B' is the complement of B, this means that it includes all elements of U that are not included in B.

If U= 23 and B= 15 then B'= U - B= 23-15= 8

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d) A'∩B

A' is the complement of A and includes all cardinalities that are outside that circle.

To know how many those are you have to do the same calculation as you did in the item before:

A'= U-A= 23-14= 9

From those 9 cardinalities only 6 are shared by both A' and B so,

A'∩B=6

e) A'∩B'

A'= 9

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A'∩B'= 9+8= 17

7 0
1 year ago
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