13.1.2. Tutorial 2: Part 1

Try these first

1. 1.

   Define what a predicate is in your own words.

   Hint

   Think about how predicates express properties like being a student or being a math major.

2. 2.

   What does the existential quantifier symbolize?

   Hint

   Remember it corresponds to 'some' in everyday language.

3. 3.

   What is a predicate in logic?

   • A type of quantifier
   • A statement about an object
   • A combination of premises

   Hint

   Think of predicates defining properties, such as 'is a student'.

4. 4.

   True or False: A counterexample can invalidate a general statement.

   • True
   • False

   Hint

   Consider the role of counterexamples in proving statements wrong.

5. 5.

   You have a group of students where 5 are math majors, and 3 are seniors. Is it possible to conclude any statement about their intersection using predicates? Create a relevant logical expression.

   Hint

   Focus on how you can relate the two groups in a logical expression.

6. 6.

   Construct a proof showing that if a student is not a senior, they cannot graduate. Use predicates and quantifiers to represent your logic.

   Hint

   Pay close attention to the contrapositive of the statement.