What is the rule h*(x+y) = (y+x)*h called?a)Commutativity ruleb)Associ...
Commutativity Rule
The rule h*(x y) = (y x)*h is called the Commutativity Rule. This rule is an important property that applies to certain operations in mathematics. It states that the order of the operands does not affect the result of the operation.
Explanation
To understand the commutativity rule and why the given equation represents it, let's break it down step by step:
1. h*(x y):
- The expression h*(x y) represents the operation of applying the function h to the two variables x and y.
- The function h can be any mathematical function or operation.
2. (y x)*h:
- The expression (y x)*h represents the operation of applying the function h to the two variables y and x.
- Here, we have reversed the order of the variables compared to the previous expression.
3. Commutativity Rule:
- The commutativity rule states that for certain operations, such as addition and multiplication, changing the order of the operands does not change the result.
- In this case, the commutativity rule is applied to the function h, which means that the order in which the variables are passed to the function does not affect the output.
4. Example:
- Let's consider a simple example to illustrate the commutativity rule.
- Suppose h represents the addition operation, and we have h*(x y) = x + y.
- Applying this rule, we can rearrange the variables: (y x)*h = y + x.
- As we can see, regardless of the order of x and y, the result of the addition operation remains the same.
Conclusion
The commutativity rule, represented by the equation h*(x y) = (y x)*h, states that the order of the operands does not affect the result of the operation. This rule is applicable to various mathematical operations, allowing us to rearrange the operands without changing the outcome. It is an important property to understand and utilize in various fields of mathematics and engineering.