Meaning And Examples of Converse Statements
Different types of statements are used in mathematics to convey certain theorems, corollaries, or prove some ideas. One such statement is the converse statement.
Converse vs. Inverse
In inverse statements, the opposite of the original hypothesis and conclusion is written, whereas in a converse statement, only the hypothesis and the conclusion is exchanged. The meaning of the statement does not change in an inverse statement.
A very important type of statement, the converse statement is mostly used in geometrical theorems. Understanding or writing a converse theorem is not very difficult.
In this Buzzle write-up, we discuss the meaning of a converse statement, how it is written, and some examples.
Converse statements are a type of conditional statements. So let us understand in brief what conditional statements are. They are basically if and then statements.
Here's an example: If it rains, then I won't go to school. The first part, i.e., if it rains is called the hypothesis, whereas the latter part then I won't go to school is called conclusion. When one condition is fulfilled, then the other condition can happen. Conditional statements are used in mathematical theorems. Sometimes, there can be two or more conditions as well.
In this Buzzle write-up, we discuss the meaning of a converse statement, how it is written, and some examples.
Converse statements are a type of conditional statements. So let us understand in brief what conditional statements are. They are basically if and then statements.
Here's an example: If it rains, then I won't go to school. The first part, i.e., if it rains is called the hypothesis, whereas the latter part then I won't go to school is called conclusion. When one condition is fulfilled, then the other condition can happen. Conditional statements are used in mathematical theorems. Sometimes, there can be two or more conditions as well.
What is a Converse Statement?
Converse statement is a statement in which the hypothesis and conclusion is interchanged. For example, statement: If the angle is less than 90º, then it is an acute angle.
Converse: If the angle is acute, it is less than 90º.
Here you can see that the hypothesis of the statement becomes the conclusion in the converse, and the conclusion becomes hypothesis.
The most important factor to be considered is that the converse statement may not be true in all cases.
For e.g.: If you are a girl, then you are a human.
Converse of this statement will be: If you are a human, then you are a girl.
It is obviously not true.
In a converse statement, the hypothesis is called 'p', and the conclusion is called 'q'. The symbol for a converse statement is as follows:
Converse: If the angle is acute, it is less than 90º.
Here you can see that the hypothesis of the statement becomes the conclusion in the converse, and the conclusion becomes hypothesis.
The most important factor to be considered is that the converse statement may not be true in all cases.
For e.g.: If you are a girl, then you are a human.
Converse of this statement will be: If you are a human, then you are a girl.
It is obviously not true.
In a converse statement, the hypothesis is called 'p', and the conclusion is called 'q'. The symbol for a converse statement is as follows:
Statement: If p, then q. (p ➔ q)Converse: If q, then p. (q ➔ p)
Examples of Converse Statements
When converse is true
1. Statement: If a number ends in 0, then it is a multiple of 10.
Converse: If a number is a multiple of 10, then it ends in 0.
Converse: If a number is a multiple of 10, then it ends in 0.
2. If the number is divisible by 2, then it is an even number.
Converse: If it is an even number, then it is divisible by 2.When converse is not true
1. Statement: If a quadrilateral is square, then it is a rectangle.
Converse: If a quadrilateral is rectangle, then it is a square.
2. Statement: If a triangle is equilateral, then it is isosceles.
Converse: If a triangle is isosceles, then it is equilateral.
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