if two angles are not supplementery, then they do not form a linear pair.
inverse
biconditional
contrapositive
The statement "if two angles are not supplementary, then they do not form a linear pair" can be rephrased as "if two angles form a linear pair, then they are supplementary."
The inverse of this statement would be "if two angles are not forming a linear pair, then they are not supplementary."
The biconditional of this statement would be "two angles form a linear pair if and only if they are supplementary."
The contrapositive of this statement would be "if two angles are supplementary, then they form a linear pair."
The statement "if two angles are not supplementery, then they do not form a linear pair" can be represented symbolically as:
P: Two angles are not supplementary
Q: The angles do not form a linear pair
1. Inverse: The negation of the original statement is: "If two angles are supplementary, then they do form a linear pair." Symbolically, it can be written as: ~P → Q.
2. Biconditional: A biconditional statement combines the original statement and its converse. The biconditional statement for this would be: "Two angles are not supplementery if and only if they do not form a linear pair." Symbolically, it can be written as: P ↔ Q.
3. Contrapositive: The contrapositive of the original statement is: "If the angles form a linear pair, then they are supplementery." Symbolically, it can be written as: ~Q → ~P.
To determine the logical statement that is the contrapositive of the given statement "If two angles are not supplementary, then they do not form a linear pair," you first need to understand the concept of contrapositive.
In logic, a contrapositive is formed by interchanging the hypothesis and conclusion of a conditional statement and negating both. So, the given statement can be written in conditional form as "If A, then B," where A represents "two angles are not supplementary" and B represents "they do not form a linear pair."
The contrapositive of this statement would be "If not B, then not A," which is equivalent to "If two angles form a linear pair, then they are supplementary."
To understand how to arrive at this contrapositive statement, you can follow these steps:
1. Start with the given conditional statement: "If A, then B."
2. Negate both A and B to get "If not B, then not A."
3. Replace A and B with their corresponding meanings: "If two angles form a linear pair, then they are supplementary."
Remember, the contrapositive of a conditional statement has the same truth value as the original statement.