Practice Nested Quantifiers (9) - Nested Quantifiers = part B - Discrete Mathematics

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6 sample questions

Question 1.
Translate 'Every student in the class has a book.' into logical notation.
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Think about what 'every' implies in logic.
Question 2.
What does ∃y: P(y) mean?
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Look at the meaning of existential quantification.
3Question 3.
What does the statement '∀x: P(x) → Q(x)' imply?
- P is true for some x
- For all x
- if P is true then Q is true
- Q is true for all x
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Focus on the relationship described by the statement.
4Question 4.
True or False: The expression ∃y ∀x: M(x,y) means there is one mother for every individual.
- True
- False
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Think about how the order of quantifiers changes meaning.
Question 5.
Design a case involving nested quantifiers that represents a family structure and describe the implications.
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Focus on how individuals relate within the family.
Question 6.
Create an argument using universal and existential quantifiers to prove a theorem about friendship.
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Specify how friendship applies universally while existing uniquely.

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