# 4 Truth Functional Connectives Logic YouTube Lecture Handouts

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## 4 Truth Functional Connectives Logic

### Truth Functional Connectives 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 aren՚t 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 – when both are true or both are false and have the same truth value (if and only if) –
• Or does not cover universe (we are not covering cloudy here)
• Conjunction: And both statements must be true
• Material implication – 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)

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