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What is universal modus ponens? Explain in propositional logic.
If for all x, if P(x) then Q(x) and P(a) for a particular a, then Q(a)
How is universal modus tollens defined? Explain in propositional logic
If for all x, if P(x) then Q(x) and ~P(a) for a particular a, then ~Q(a)
If for all x, if P(x) then Q(x), and ~P(a) for a particular a, then ~Q(a) ; this argument is invalid.
What is the converse error?
If for all x, if P(x) then Q(x), and Q(a) for a particular a, then P(a) ; this argument is invalid.
How do we use diagrams in testing the validity of arguments?
Making a Venn diagram for each that represents relationships between variables
How do we prove the validity of an argument? List the steps
Express the statement to be proved in the form “For every x belonging to D, if P(x) then Q(x).”
Suppose x is an arbitrarily chosen element of D
for which P(x) is true. “Suppose
x belongs to D and P(x).”
Show that the conclusion Q(x) is true by using definitions, previously established results, and the rules for logical inference.
How to we disprove an argument using counterexample?
Find a specific instance showing that a universal statement is false where the hypothesis true and the conclusion is false.