Laws of Indices An index is a number that indicates the position of a specific element in a set of numbers. There are three main laws of indices: 1. Law of...
An index is a number that indicates the position of a specific element in a set of numbers. There are three main laws of indices:
1. Law of Index Addition:
The index of a sum is equal to the sum of the indices. For example, if you have the sets A = {1, 3, 5} and B = {2, 4, 6}, then the index of the element 1 in set A + B is 3 + 4 = 7.
2. Law of Index Multiplication:
The index of a product is equal to the product of the indices. For example, if you have the sets A = {1, 3, 5} and B = {2, 4, 6}, then the index of the element 1 in set A * B is 1 * 2 = 2.
3. Law of Index Subtraction:
The index of a difference is equal to the difference between the indices of the two elements. For example, if you have the sets A = {1, 3, 5} and B = {2, 4, 6}, then the index of the element 2 in set A - B is 3 - 4 = 1.
These laws can be used to simplify expressions, solve problems involving sets, and perform various mathematical operations