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Get Started Now- Intro Lesson8:00
- Lesson: 1a2:19
- Lesson: 1b2:19
- Lesson: 1c2:14
- Lesson: 2a4:48
- Lesson: 2b2:45
- Lesson: 2c3:08
- Lesson: 3a13:22
- Lesson: 3b8:14
- Lesson: 3c6:28
- Lesson: 3d6:42
- Lesson: 4a9:01
- Lesson: 4b5:57
- Lesson: 4c5:30
- Lesson: 4d5:29

A **biconditional** is a conjunction of a conditional and its converse. In symbolic form it would be:

$(p \to q)$ ˄ $(q \to p)$

We can also write it as $p \leftrightarrow q$. In words, we connect $p$ and $q$ with "if and only if". A biconditional can be only true if both the conditional and converse is true. Here is a truth table of a biconditional.

$p$ | $q$ | $p \to q$ | $q \to p$ | $(p \to q )$ ˄ $(q \to p)$ | $p \leftrightarrow q$ |

T | T | T | T | T | T |

T | F | F | T | F | F |

F | T | T | F | F | F |

F | F | T | T | T | T |

- IntroductionBiconditionals Overview:a)What are Biconditionals
- 1.
**Forming the Biconditional**

Write a biconditional using the given conditionals:a)If today is Monday, then yesterday was Sunday.

If yesterday was Sunday, then today is Mondayb)If he drives faster than 100 km, then he will get a ticket.

If he gets a ticket, then he has driven faster than 100 km.c)If today is the weekend, then I do not go to school.

If I do not go to school, then it is the weekend. - 2.You are given 3 statements in symbolic form:

$p$: There is cream in milk

$q$: There is milk in coffee

$r$: There is cream in coffeea)Write the conditional $(p$ ˄ $q)$ $\to$ $r$ in words.b)Write the converse$(p$ ˄ $q)$ $\to$ $r$ in words.c)Write the biconditional. - 3.
**Truth value of Biconditionals**

Determine the truth value of the following biconditionals:a)$x = 5$. if and only if $x + 7 = 12$.b)If $x > 5$, if and only if $x > 2$.c)The triangle is an isosceles, if and only if two sides are equal.d)The angle is acute, if and only if the angle is less than 90° degrees. - 4.Let both $p$, $q$ and $r$ be statements.a)If $p$ is true, $q$ is true and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?b)If $p$ is false, $q$ is true and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?c)If $p$ is false, $q$ is false and $r$ is true, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?d)If $p$ is false, $q$ is false and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?