Original	Inverse	Contrapositive
p	q	~p	~q	p → q	~p → ~q	~q → ~p
TRUE	TRUE	FALSE	FALSE	TRUE	TRUE	TRUE
TRUE	FALSE	FALSE	TRUE	FALSE	TRUE	FALSE
FALSE	TRUE	TRUE	FALSE	TRUE	FALSE	TRUE
FALSE	FALSE	TRUE	TRUE	TRUE	TRUE	TRUE

Solved Questions on Converse Statement

Example 1: If all squares are rectangles, are all rectangles squares?

Converse: If a shape is a rectangle, then it is a square.

Solution:

The original statement says that all squares are rectangles. This is true because a square, by definition, has four sides of equal length and four right angles, making it a special type of rectangle where all sides are equal. However, the converse statement is not necessarily true. Not all rectangles are squares because rectangles can have unequal side lengths, whereas squares have all sides equal. Therefore, the converse statement is false.

Example 2: If all right angles are 90 degrees, are all 90 degree angles right angles?

Converse: If an angle measures 90 degrees, then it is a right angle.

Solution:

The original statement is true because a right angle, by definition, measures 90 degrees. However, the converse statement is also true. If an angle measures 90 degrees, then it must be a right angle, as any angle measuring exactly 90 degrees forms a perfect right angle.

Example 3: If a number is divisible by 3, then it is an odd number.

Converse: If a number is an odd number, then it is divisible by 3.

Solution:

The original statement is false. While it is true that all odd numbers are not divisible by 2, they are not necessarily divisible by 3. For example, the number 5 is an odd number but is not divisible by 3. Therefore, the converse statement is also false because not all odd numbers are divisible by 3.

Example 4: If a shape has four sides, then it is a quadrilateral.

Converse: If a shape is a quadrilateral, then it has four sides.

Solution:

The original statement is true. A quadrilateral is defined as a polygon with four sides, so any shape with four sides is indeed a quadrilateral. Similarly, the converse statement is true. If a shape is a quadrilateral, then it must have four sides because that is a defining characteristic of a quadrilateral. Therefore, both the original statement and its converse are true.

Converse Statement: Practice Questions

Q1: If all birds have wings, do all winged creatures have beaks?

Q2: If all triangles have three sides, do all polygons with three sides have to be triangles?

Q3: If all vehicles are cars, are all cars vehicles?

Converse Statement: FAQs

What is Conditional Statement?

A conditional statement is a fundamental concept in logic and mathematics where a hypothesis is followed by a conclusion, often represented as “If p, then q.”

What is the Converse of a Statement?

The converse of a statement is formed by interchanging the antecedent and the consequent of a conditional statement. For example, if the original statement is “If it is raining, then the ground is wet,” the converse would be “If the ground is wet, then it is raining.”

How do Mathematicians Use Converse?

Mathematicians use the converse of a statement to explore the logical relationships between different assertions. By examining both the original statement and its converse, mathematicians can gain a deeper understanding of implications and relationships within a given context.

Is a Conditional Statement Logically Equivalent to a Converse and Inverse?

A conditional statement is not logically equivalent to its converse or inverse. While a conditional statement asserts a specific relationship between two events or conditions, the converse and inverse statements may or may not hold true in the same context.

Do the Converse and the Inverse Have The Same Truth Value?

The truth value of the converse and the inverse may differ from that of the original conditional statement. In some cases, the converse and the inverse of a true conditional statement may also be true, but this is not always the case. Each statement must be evaluated independently to determine its truth value.