9.3. Translating Statements with Nested Quantification

Try these first

1. 1.

   Translate the statement: 'All dogs bark.'

   Hint

   Think about the meaning of 'all' and how it relates to 'bark'.

2. 2.

   What does ∃x (Bird(x) ∧ CanFly(x)) express?

   Hint

   Focus on the meaning of 'there exists' and how it relates to different properties.

3. 3.

   Which of the following is the correct translation of 'Every person has a mother'?

   • ∃x M(x,y)
   • ∀x ∃y M(x,y)
   • ∃y ∀x M(x,y)

   Hint

   Focus on who the statement refers to and the relationship defined.

4. 4.

   True or False: Changing the order of quantifiers does not affect the meaning of a statement.

   • True
   • False

   Hint

   Think of how reversing statements changes conditions or relationships.

5. 5.

   A city has citizens who are parents. Formulate: 'Every citizen is a parent to at least one child, and each child has a unique parent.'

   Hint

   Break the requirements into parts and translate them logically.

6. 6.

   If all fruits are sweet, and some apples are fruits, what can you conclude about apples?

   Hint

   Consider the implications of the universal statement on the specific example.