- #1
Ella087
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Prove by induction that the number of 2-subsets of an n-set A equals n(n-1)/2.
An n-Set is a set that contains n elements. The number n can be any positive integer.
The formula n(n-1)/2 represents the number of 2-subsets that can be formed from an n-set. To prove this, we can use the combinatorial approach. We know that the number of ways to choose 2 elements from a set of n elements is n choose 2, which is also equal to n(n-1)/2. Therefore, the 2-subsets of an n-Set A equals n(n-1)/2.
Sure, let's say we have a set A = {1, 2, 3, 4}. The number of 2-subsets that can be formed from this set is 4 choose 2, which is equal to 6. Using the formula n(n-1)/2, we get 4(4-1)/2 = 6. So, the number of 2-subsets of A equals n(n-1)/2.
No, the formula only works for finding the number of 2-subsets in an n-set. To find the number of subsets with more than 2 elements, we can use the formula 2^n - 1, where n is the number of elements in the set.
Proving this formula is important because it helps us understand the relationship between the number of elements in a set and the number of 2-subsets that can be formed from that set. It also allows us to solve problems related to combinations and permutations, which have various applications in mathematics, computer science, and other fields.