How many subsets can be formed from the letters in the word cat? - briefly
To determine the number of subsets that can be formed from the letters in the word "cat," we need to consider all possible combinations of its letters. The word "cat" consists of 3 unique letters. The total number of subsets for a set with ( n ) elements is given by ( 2^n ). Therefore, for the word "cat," the number of subsets is ( 2^3 = 8 ).
This includes the empty set and subsets containing one, two, or all three letters.
How many subsets can be formed from the letters in the word cat? - in detail
To determine the number of subsets that can be formed from the letters in the word "cat," we need to understand the concept of subsets in set theory. A subset is a set whose elements are all elements of another set. This includes the empty set and the set itself. The word "cat" consists of three distinct letters: 'c', 'a', and 't'.
The total number of subsets of a set with 'n' elements is given by (2^n). This is because each element can either be included in a subset or excluded from it, leading to two choices per element. For the word "cat," which has three letters, the number of subsets is (2^3 = 8).
Let's list all possible subsets of the letters in "cat":
- The empty set: (\emptyset)
- Subsets with one element:
- {'c'}
- {'a'}
- {'t'}
- Subsets with two elements:
- {'c', 'a'}
- {'c', 't'}
- {'a', 't'}
- The subset with all three elements:
- {'c', 'a', 't'}
These eight subsets cover all possible combinations of the letters 'c', 'a', and 't'. Each subset is a valid combination, including the empty set and the set containing all three letters.
In summary, the number of subsets that can be formed from the letters in the word "cat" is 8. This result is derived from the fundamental principle of set theory, which states that for a set with 'n' distinct elements, there are (2^n) possible subsets.