if two angles are supplentary, then they are form a linear pair
contrapositive
biconditional
inverse
converse
converse
The contrapositive of the statement "if two angles are supplementary, then they form a linear pair" is:
Contrapositive: If two angles do not form a linear pair, then they are not supplementary.
The biconditional of the statement is:
Biconditional: Two angles form a linear pair if and only if they are supplementary.
The inverse of the statement is:
Inverse: If two angles are not supplementary, then they do not form a linear pair.
The converse of the statement is:
Converse: If two angles form a linear pair, then they are supplementary.
To understand the terms contrapositive, biconditional, inverse, and converse, let's first define what they mean in relation to logic statements.
A logical statement is a sentence that can either be true or false. In mathematics, logical statements often involve conditions or relationships between objects or properties.
1. Contrapositive:
The contrapositive of a statement is formed by negating both the hypothesis (the part following the "if") and the conclusion (the part following the "then") of the original statement, and then reversing their order.
For example, the contrapositive of the statement "If two angles are supplementary, then they form a linear pair" is "If two angles do not form a linear pair, then they are not supplementary."
To find the contrapositive of a statement, follow these steps:
- Negate the hypothesis and the conclusion of the original statement.
- Reverse the order of the negated hypothesis and conclusion.
2. Biconditional:
A biconditional statement (also known as the "if and only if" statement) is a statement in which the occurrence of one condition is dependent on the occurrence of another condition, and vice versa.
For example, the biconditional statement for the original statement would be: "Two angles are supplementary if and only if they form a linear pair."
To form a biconditional statement, follow these steps:
- Write the original statement as an "if" statement: "If two angles are supplementary, then they form a linear pair."
- Reverse the order and write a second "if" statement: "If two angles form a linear pair, then they are supplementary."
- Combine the two "if" statements with an "if and only if" connector: "Two angles are supplementary if and only if they form a linear pair."
3. Inverse:
The inverse of a logical statement is formed by negating both the hypothesis and the conclusion of the original statement.
For example, the inverse of the original statement "If two angles are supplementary, then they form a linear pair" is "If two angles are not supplementary, then they do not form a linear pair."
To find the inverse of a statement, follow these steps:
- Negate the hypothesis and the conclusion of the original statement.
4. Converse:
The converse of a logical statement is formed by reversing the order of the hypothesis and the conclusion of the original statement.
For example, the converse of the original statement "If two angles are supplementary, then they form a linear pair" is "If two angles form a linear pair, then they are supplementary."
To find the converse of a statement, reverse the order of the hypothesis and the conclusion.
It is important to note that while a conditional statement and its converse have the same logical form, they are not always logically equivalent. The same applies to the contrapositive and the inverse.