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Fun with Logic!
Transcript of Fun with Logic!
Implication means that if the antecedent (first proposition) of the conditional is true, then the consequent (last proposition) must also be true.
A conditional is true when this relationship is so.
Connects two or more atomic propositions to make a conjunction
Connects two or more propositions to make a conditional.
Any number of atomic propositions may be connected by 'if/then' to make a conditional,
AS LONG AS the antecedent always implies the consequent.
Any number of atomic propositions may be connected in any order by 'or' to make a disjunction.
A disjunction is true if at least one part of it is true.
When 'or' is used in an inclusive sense, more than one part may be true.
When 'or' is used in an exclusive sense, only one part may be true.
Any number of atomic propositions may be connected in any order by '&' to make a conjunction.
A conjunction is true only if ALL of its parts are true.
If one part is false, then the whole conjunction is false.
Variables which stand in for any atomic proposition:
sentence or statement of fact
Connects two or more propositions to make a disjunction
Connects two propositions to make a disjunction in which at least one part must be false
Negates a proposition; gives it the opposite truth value
signifies a conclusion
'if and only if'
Connects two propositions to make a bi-conditional
And when this relationship is so, and the consequent is FALSE, then the antecedent must also be false.
If the antecedent and consequent are so related that they are always either both true or both false,
then their relationship is called a bi-conditional.