Practice Universal Quantification (8. 1.4.2) - Predicate Logic - Discrete Mathematics

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6 sample questions

Question 1.
Explain what universal quantification means.
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Think about the notation ∀x.
Question 2.
Provide a simple example of a universally quantified statement.
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Consider what numbers are included in the natural numbers.
3Question 3.
What does the notation ∀x, P(x) represent?
- For all x
- P(x) is true
- There exists an x such that P(x) is true
- P(x) holds for some x
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Remember the symbol used!
4Question 4.
True or False: Universal quantification is the same as existential quantification.
- True
- False
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Think about what each quantifier states.
Question 5.
Consider the predicate P(x): 'x is a square number'. What can you deduce about ∀x, P(x) in the domain of all integers?
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Consider known square numbers.
Question 6.
Prove or disprove: ∀x, (x + 2 > x) is true for all integers.
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Think about the properties of integers.

4 more questions in this section. Enroll free to practise them all.