What are conditional and biconditional statements?
A conditional statement is of the form “if p, then q,” and this is written as p → q. A biconditional statement is of the form “p if and only if q,” and this is written as p ↔ q. For a condtional statement p → q, the converse is q → p, the contrapositive is ¬q → ¬p, and the inverse is ¬p → ¬q.
What is the symbol for biconditional?
A biconditional is true if and only if both the conditionals are true. Bi-conditionals are represented by the symbol ↔ or ⇔ .
What is an example of biconditional?
If I have a pet goat, then my homework will be eaten. If I have a triangle, then my polygon has only three sides. If the polygon has only four sides, then the polygon is a quadrilateral. If I eat lunch, then my mood will improve.
What is the symbol for disjunction?
∨
The two types of connectors are called conjunctions (“and”) and disjunctions (“or”). Conjunctions use the mathematical symbol ∧ and disjunctions use the mathematical symbol ∨ .
What does conditional mean in geometry?
Conditional Statements. A statement joining two events together based on a condition in the form of “If something, then something” is called a conditional statement. In Geometry, conditional statements, which are also called “If-Then” statements, are written in the form: If p, then q.
What are the 4 conditional statements?
There are 4 basic types of conditionals: zero, first, second, and third.
What are the parts of a conditional statement?
A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. For instance, “If it rains, then they cancel school.”
What is the meaning of p q?
The statement “p implies q” means that if p is true, then q must also be true. Statement pis called the premise of the implication and q is called the conclusion.
What is the converse of a biconditional statement?
Because the statement is biconditional (conditional in both directions), we can also write it this way, which is the converse statement: Conclusion if and only if hypothesis. Notice we can create two biconditional statements. If conditional statements are one-way streets, biconditional statements are the two-way streets of logic.
How do you write two biconditional statements?
Since both statements are true, we can write two biconditional statements: You can do this if and only if both conditional and converse statements have the same truth value. They could both be false and you could still write a true biconditional statement (“My pet goat draws polygons if and only if my pet goat buys art supplies online.”).
How do you use conditional statements in logic?
In logic, concepts can be conditional, using an if-then statement: If I have a pet goat, then my homework will be eaten. If I have a triangle, then my polygon has only three sides. If I eat lunch, then my mood will improve.
How do you replace a conditional statement with a hypothesis?
So the conditional statement, “If I have a pet goat, then my homework gets eaten” can be replaced with a p p for the hypothesis, a q q for the conclusion, and a → → for the connector: For biconditional statements, we use a double arrow, ⇔ ⇔, since the truth works in both directions: