Practice Multi-valued Predicate Functions (8. 1.3) - Predicate Logic - Discrete Mathematics

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6 sample questions

Question 1.
What is a predicate function?
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Think about how it describes elements.
Question 2.
Define universal quantification.
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It starts with a symbol that often resembles a loop.
3Question 3.
What does the notation ∀x P(x) mean?
- P(x) holds for some x.
- P(x) holds for all x.
- P(x) is always false.
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Consider how it encompasses all elements.
4Question 4.
True or False: Existential quantification asserts that a predicate is true for every element in a domain.
- True
- False
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Think about ‘at least one’ versus ‘all’.
Question 5.
Given the predicates P(x) = (x^2 > 0) and Q(x) = (x ≠ 0), prove that ∀x(P(x) → Q(x)).
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Examine the conditions under which P will lead to Q. Just analyze both predicates together.
Question 6.
Create an example where universal quantification fails in certain domains while holding true in others.
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Try out edge cases when including boundary values.

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