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

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

Truth Functional Connectives
Connective & SymbolProposition & ComponentExample
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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