The three most common ways to change a conditional statement are by taking its inverse, its converse statement, or its contrapositive. In each case, either the hypothesis or the conclusion swap places, or a statement is replaced by its negation.
The Inverse Statement
A conditional statement is reversed by replacing the hypothesis and the conclusion with their negations. In the case of the statement, “A vertex that is confined to a circle is called an inscribed angle”, the converse of the statement is “A vertex that isn’t confined to a circle is called an ungrounded angle.” Both the hypothesis and the conclusion were negated. If the original statement reads “if j, then k“, then the reverse would be, “if not j, then not k.”
It is not possible to determine the true inverse of a statement. The inverse of some statements may have the same truth value as the inverse of another statement and vice versa. The statement “A four-sided polygon is a quadrilateral” and its inverse, “A polygon with more or fewer sides than four sides is not a quadrilateral,” are both true (the truth value of each is T). The original statement and its inverse, however, are not equally true in the inscribed angles example above. It is true that an angle with its vertex on a circle will not be an inscribed angle, but the converse is false: it is possible for an angle with its vertex on a circle to still not be an inscribed angle.
The Converse Statement
By switching the hypothesis and conclusion, the converse of a statement can be formed. Conversely, “If two lines don’t intersect, then they are parallel” is “If two lines are parallel, then they don’t intersect.” The converse of “if p, then q” is “if q, then p.”
A statement’s converse may or may not have the same meaning as its original. A tiger is a mammal, for instance, so the converse would be a mammal is a tiger. That’s certainly not the case.
In all cases, however, a definition must have a contrarian interpretation. If this is not the case, then the definition is not valid. For example, we know the definition of an equilateral triangle well: “if all three sides of a triangle are equal, then the triangle is equivalent.” As a result, “If a triangle is equivalent, it has three equal sides.” But what if we put this test to the test with a wrong definition on it? If we incorrectly stated the definition of a tangent line as: “A tangent line crosses a circle,” the statement would be true. However, the converse, “A line that intersects a circle is a tangent line”, is incorrect; the converse could describe a secant line as well. Therefore, the converse is very helpful in determining the validity of a definition.
What Is A Converse Statement?
A converse statement is obtained by reversing the hypothesis and conclusion of a conditional statement.
Understanding “hypothesis” and “conclusion” is important.
A statement which is of the form of “if p then q” is a conditional statement, where ‘p’ is called the hypothesis and ‘q’ is called the conclusion.
If something is negated, it means it conveys the opposite of that thing.
Converse is a statement derived by reversing a statement’s hypothesis and conclusion.