How many different integers represent the sum of two or more members of the set {-4,-3,-2,-1,0,1,2,3,4}?
To find out how many different integers represent the sum of two or more members of the given set, we can use the concept of combinations.
First, we need to generate all the possible combinations by adding two or more numbers from the set.
Let's consider all the subsets of the given set and find their sums:
Subset 1: {-4}
Sum = -4
Subset 2: {-3}
Sum = -3
Subset 3: {-2}
Sum = -2
Subset 4: {-1}
Sum = -1
Subset 5: {0}
Sum = 0
Subset 6: {1}
Sum = 1
Subset 7: {2}
Sum = 2
Subset 8: {3}
Sum = 3
Subset 9: {4}
Sum = 4
Subset 10: {-4, -3}
Sum = -7
Subset 11: {-4, -2}
Sum = -6
Subset 12: {-4, -1}
Sum = -5
Subset 13: {-4, 0}
Sum = -4
Subset 14: {-4, 1}
Sum = -3
Subset 15: {-4, 2}
Sum = -2
Subset 16: {-4, 3}
Sum = -1
Subset 17: {-4, 4}
Sum = 0
Subset 18: {-3, -2}
Sum = -5
Subset 19: {-3, -1}
Sum = -4
Subset 20: {-3, 0}
Sum = -3
Subset 21: {-3, 1}
Sum = -2
Subset 22: {-3, 2}
Sum = -1
Subset 23: {-3, 3}
Sum = 0
Subset 24: {-3, 4}
Sum = 1
Subset 25: {-2, -1}
Sum = -3
Subset 26: {-2, 0}
Sum = -2
Subset 27: {-2, 1}
Sum = -1
Subset 28: {-2, 2}
Sum = 0
Subset 29: {-2, 3}
Sum = 1
Subset 30: {-2, 4}
Sum = 2
Subset 31: {-1, 0}
Sum = -1
Subset 32: {-1, 1}
Sum = 0
Subset 33: {-1, 2}
Sum = 1
Subset 34: {-1, 3}
Sum = 2
Subset 35: {-1, 4}
Sum = 3
Subset 36: {0, 1}
Sum = 1
Subset 37: {0, 2}
Sum = 2
Subset 38: {0, 3}
Sum = 3
Subset 39: {0, 4}
Sum = 4
Subset 40: {1, 2}
Sum = 3
Subset 41: {1, 3}
Sum = 4
Subset 42: {1, 4}
Sum = 5
Subset 43: {2, 3}
Sum = 5
Subset 44: {2, 4}
Sum = 6
Subset 45: {3, 4}
Sum = 7
As we can see, there are a total of 45 different sums of two or more members of the set {-4, -3, -2, -1, 0, 1, 2, 3, 4}.