# 4 Truth Functional Connectives Logic YouTube Lecture Handouts

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## 4 Truth Functional Connectives Logic

### Truth Functional Connectives

- A
**negation**is a proposition asserting that another proposition is*false*. - A
**conjunction**is a proposition asserting that two other propositions are*both true*. - A
**disjunction**is a proposition asserting that*at least one*of two propositions is true. - A
**conditional**is a proposition asserting that*if*one proposition is true,*then*so is another. - A
**biconditional**is a proposition asserting that two propositions are either both true and both false. (In other words, one is true*if and only if*the other is true.)

A **simple proposition** is one that contains no truth-functional connectives. A proposition is **compound** if it contains one or more truth-functional connectives.

Compound proposition - If roses are red and violets are blue, then roses arenΥt red

Connective & Symbol | Proposition & Component | Example |

And () | Conjunction (conjuncts) | It is cloudy and rainy |

Or () | Disjunction (disjuncts) | It is sunny or it is rainy |

If Then () | Conditional (Antecedent & Consequent) | If there is smoke, then there is fire |

If and only If | Biconditional (components) | I will go to watch championship if and only if I get ticket |

- Material equivalence β when both are true or both are false and have the same truth value (if and only if) β
- Or does not cover universe (we are not covering cloudy here)
- Conjunction: And both statements must be true
- Material implication β if then is weak relation p materially implies q is true when either p is false or q is true
- Each component of conjunction is conjunct (it is cloudy) (it is rainy)

β Manishika