Practice Order Of Quantification (9.2) - Nested Quantifiers = part B - Discrete Mathematics

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6 sample questions

Question 1.
What does the universal quantifier (∀) signify?
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Think about what it covers in a group!
Question 2.
How would you express that 'some person is a parent' logically?
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Remember this quantifier indicates at least one!
3Question 3.
What does the statement 'For all x, P(x)' imply?
- That at least one x satisfies P(x)
- That all x satisfy P(x)
- That no x satisfy P(x)
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It’s the opposite of the existential quantifier!
4Question 4.
If 'There exists an x such that P(x)' is true, what can you conclude?
- True
- False
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Think of it as finding at least one match.
Question 5.
Construct a logical statement combining all relationships suggested in 'Every cat has one owner, but not every owner has a cat.'
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Think about both universal and existential quantifications.
Question 6.
Propose a statement that illustrates a counterexample to the claim 'if someone is a parent, then they have at least one child.'
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Explore real-world exceptions.

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