What is the biconditional inverse converse and Contrapositive statements?
What is the biconditional inverse converse and Contrapositive statements?
If the “if-then” statement is true, then the contrapositive is also true. The contrapositive is logically equivalent to the original statement. The converse and inverse may or may not be true. When the original statement and converse are both true then the statement is a biconditional statement.
What is converse and biconditional?
Converse and compound statements can both be biconditional statements: A conditional statement is a logic statement that includes the phrase, “if-then.” For example, “If a polygon has three sides, then it must be a triangle.” A converse statement is when you flip the order of the original statement.
What are converse and inverse statements?
If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true….Converse, Inverse, Contrapositive.
| Statement | If p , then q . |
|---|---|
| Converse | If q , then p . |
| Inverse | If not p , then not q . |
| Contrapositive | If not q , then not p . |
What is an example of an inverse statement?
Our inverse statement would be: “If it is NOT raining, then the grass is NOT wet.” Our contrapositive statement would be: “If the grass is NOT wet, then it is NOT raining.”
What does inverse mean in logic?
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form , the inverse refers to the sentence. .
What is meant by contrapositive?
: a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them “if not-B then not-A ” is the contrapositive of “if A then B “
Does inverse mean opposite?
In mathematics, the word inverse refers to the opposite of another operation. Let us look at some examples to understand the meaning of inverse. Example 1: Hence, addition and subtraction are opposite operations.
Is an inverse logically equivalent?
. Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other.