Biconditional Operator
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Type classification: this is a lesson resource. |
Welcome! This is a lesson in the Introductory Discrete Mathematics for Computer Science course here at Wikiversity.
Previous lesson: Conditional Operator
Your Last Operator![edit]
The biconditional operator looks like this:
It is a diadic operator. You'll learn about what it does in the next section.
Compound Propositions and Logical Equivalence[edit]
Now you will be introduced to the concepts of logical equivalence and compound propositions.
- Compound propositions involve the assembly of multiple statements, using multiple operators.
- Logical equivalence means that the truth tables of two statements are the same.
The biconditional operator is sometimes called the "if and only if" operator. = TRUE means that the truth values of p and q are the same. "You will see the notes for this class if and only if someone shows them to you" is an example of a biconditional statement.
- If someone shows you the notes and you see them, the statement is true.
- If someone shows you the notes and you do not see them, the biconditional statement is violated. Therefore, a value of "false" is returned.
- If no one shows you the notes and you see them, the biconditional statement is violated. Therefore, a value of "false" is returned.
- If no one shows you the notes and you do not see them, a value of true is returned.
- The biconditional statement is logically equivalent to !
Truth Table for the Biconditional[edit]
T | T | T |
T | F | F |
F | T | F |
F | F | T |
Next Lesson[edit]
The next lesson is called Compound Propositions and Useful Rules.