4 Truth Functional Connectives Logic YouTube Lecture Handouts
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4 Truth Functional Connectives: And, Or, If Then, If & Only If - Logic
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