Plz explain all the properties of inequality.....required in increasing and decreasing functions.
Dear Student,
There are many properties of inequalities.
It is not possible to mention all unless asked for some specific ones.
Here are some basic properties of inequality.
There are four inequalities [(less than)], [(greater than)], [(less than or equal to)], [(greater than or equal to)]. The properties of inequalities are:
Let a, b, c be real numbers.
- Transitive Property: If and then . Similarly, if and then .
- Reversal Property: If then . Similarly, if then .
- Law of Trichotomy: Only one of the following is true: .
- Addition Property: If then . Similarly, if then .
- Subtraction Property: If then . Similarly, if then .
- Multiplication Property: If and c is positive then and if and c is negative then . Similarly, If and c is positive then and and c is negative then .
- Division Property: If and c is positive then and if and c is negative then . Similarly, If and c is positive then and and c is negative then .
- Additive Inverse: If then . Similarly, if then .
- Multiplicative Inverse: If then . Similarly, if then .
- Non-negative Property of Squares: A square of a number is always greater than or equal to zero.
- Square Root Property: If then . Similarly, If then
Regards.