- #1
Kolmogorov
- 7
- 0
Problem:
-The Union of set A, set B and set C has 104 elements.
-The Union of Set A and B has 51 elements
-The Union of Set A and C has 84 elements
-The Union of Set B and C has 97 elements
-The Intersection of Set A and the Union of Set B and C has 17 elements.
-Set C has twice as many elements as set B and three times as many elements as Set A.
How many elements does A have?
Hint: Take C is 6x and solve for x.
This is what I did after drawing a Venn diagram:
A minus B[itex]\cup[/itex]C = 104-97=7
B minus A[itex]\cup[/itex]C = 104-84=20
C minus A[itex]\cup[/itex]B = 104-51=53
If you add up these numbers and subtract them from 104, you'll get that all the intersections of these sets together have 24 elements.
It is given that A[itex]\cap[/itex](B[itex]\cup[/itex]C) = 17.
Therefore, the intersection of B and C without whatever is in A, should be 7.
From this fact the elements of A can be calculated from the fact that A[itex]\cup[/itex]C has 84 elements. To calculate the elements of A take 84 and subtract the elements of C that are not in A, 84 -53 -7= 24
I didn't use the hint nor did I use the size relationship between the sets, so I am not sure if I did this problem right.
How could I solve this problem with the hint (solve as an equation of x) and the given relationship between A, B and C?
-The Union of set A, set B and set C has 104 elements.
-The Union of Set A and B has 51 elements
-The Union of Set A and C has 84 elements
-The Union of Set B and C has 97 elements
-The Intersection of Set A and the Union of Set B and C has 17 elements.
-Set C has twice as many elements as set B and three times as many elements as Set A.
How many elements does A have?
Hint: Take C is 6x and solve for x.
This is what I did after drawing a Venn diagram:
A minus B[itex]\cup[/itex]C = 104-97=7
B minus A[itex]\cup[/itex]C = 104-84=20
C minus A[itex]\cup[/itex]B = 104-51=53
If you add up these numbers and subtract them from 104, you'll get that all the intersections of these sets together have 24 elements.
It is given that A[itex]\cap[/itex](B[itex]\cup[/itex]C) = 17.
Therefore, the intersection of B and C without whatever is in A, should be 7.
From this fact the elements of A can be calculated from the fact that A[itex]\cup[/itex]C has 84 elements. To calculate the elements of A take 84 and subtract the elements of C that are not in A, 84 -53 -7= 24
I didn't use the hint nor did I use the size relationship between the sets, so I am not sure if I did this problem right.
How could I solve this problem with the hint (solve as an equation of x) and the given relationship between A, B and C?
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