Module 07 : Direct Proofs

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10 Terms

1
What does universal instantiation state?
If a property is true of everything in a set, then it is true of any particular thing in the set.
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2
Provide an example of universal instantiation.
If 'All men are mortal' and 'Socrates is a man', then 'Socrates is mortal'.
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3

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)

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4

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)

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5
What is the inverse error?

If for all x, if P(x) then Q(x), and ~P(a) for a particular a, then ~Q(a) ; this argument is invalid.

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6

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.

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7

How do we use diagrams in testing the validity of arguments?

Making a Venn diagram for each that represents relationships between variables

<p>Making a Venn diagram for each that represents relationships between variables</p>
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8

How do we prove the validity of an argument? List the steps

  1. Express the statement to be proved in the form “For every x belonging to D, if P(x) then Q(x).”

  2. Suppose x is an arbitrarily chosen element of D
    for which P(x) is true. “Suppose
    x belongs to D and P(x).”

  3. Show that the conclusion Q(x) is true by using definitions, previously established results, and the rules for logical inference.

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9

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.

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10
What is the definition of an even integer?
An integer n is even if and only if n equals twice some integer.
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