quick SAT math question?

Question

The union set A, B and C is {1,2,3,4,5,6,7}, the intersection of Sets A, B, and C is {0}, (empty set) and Set A= {1,2,3,4}. If Set B contains a greater number of elements than does Set C, what is the largest possible value of the sum of the elements of Set B?

any ideas on how to do this?

what is the empty set & intersection?

Answer 1

First of all {0} is not the empty set. The empty set is a set that has nothing.

Intersection of sets means finding things which are common in all the sets. So if the intersection of A B and C is empty then the sets have nothing in common. To maximize B, we set C as the empty set. Thus B would have to be {5,6,7}. So the sum of the elements of set B=5+6+7=18. Some people above did not take into consideration that C can be an empty set. Raymond did not take into consideration that the intersection of A B and C is empty.

Answer 2

intersection: elements that belong to all sets.

empty set: a set that contains nothing (not even the number 0).

I'd try an easy way out: make set C empty. Then any intersection with C must be empty (there cannot be, ever, any element that belongs to A and B AND C, since C contains nothing).
C being empty, then it contains zero elements. If B contains anything, then B must contain more elements than C.

B must contain something, because the union (elements that belong to at least one set) contains 7, which is neither in A nor in C; therefore 7 must belong to B.
As a minimum, B must contain 5, 6, 7.

B could also contain other elements, as long as these are in the union. For example, 1 could belong in B. Because it is not in C, that would still leave the intersection empty. 1 would still belong to the union, because 1 is in "at least" one set.

So, make B = {1, 2, 3, 4, 5, 6, 7}

and the sum of B's elements is 28.

Do we satisfy all criteria?
union is {1, 2, 3, 4, 5, 6, 7}? OK
intersection is empty? OK because C is empty
B has more elements than C? OK B has 7 while C has none.

Answer 3

If set C is an emplty set, then you can have the largest possible value of the sum of the elements of set B {1, 2, 3, 4, 5, 6, 7}.
sum = 28
---------
Check:
B = {1, 2, 3, 4, 5, 6, 7} contains a greater number of elements than C which is empty.
A and B and C = empty set, since C is an empty set.
A or B or C = {1, 2, 3, 4, 5, 6, 7}.

Answer 4

13
Since there is no intersection, B and C make up 5,6,7
Since B has more than C and the 2 highest are 6 and 7....6+7=13

Further, The intersection is what all sets A B and C would have in common. Since this is an "empty set" or nothing...each number 1 through 7 falls into eithe A B or C. if a is 1,2,3,4.....that only leaves 5,6,7 for both B and C sets

Answer 5

To say that those sets have an intersection equaling the empty set means that there are no elements that are in all the sets A, B, and C.

Since A = {1,2,3,4} then B u C = {5,6,7}. There are no elements in both B and C and B has more elements that C, then B = {5,6} or {5,7} or {6,7}. You want to maximize the sum of the elements of B, so pick the one with the largest values = {6,7}.

Answer 6

union means A or B or C.
intersection means A and B and C.

if A = {1, 2, 3, 4}, B and C must = {5, 6, 7}.

the greatest two integers: B = {6,7} = 6+7 = 13

Answer 7

18.

(5+6+7)