Predicate Logic Self Assessment Instructions Instructions: These problems are provided for your own self-assessment. You need to work on them alone, solve them without looking at the solution, and...

4 maths questions as attached


Predicate Logic Self Assessment Instructions Instructions: These problems are provided for your own self-assessment. You need to work on them alone, solve them without looking at the solution, and only then compare your solution with the provided one. You do not need to solve all of these problems. Please solve at least 4 of them without mistake. Not only should your answer be correct, but your reasons should also match the solution. Do not be sloppy in your self-marking. In each of these tasks: 1. List and match all the predicates and quantifiers, the quantified variables and the domain of each variable. 2. Determine the truth value of the statement. 3. Justify rigorously your explanation. Submit your evidence of self-assessment by showing your work and self-correction. There are a limited number of exercises. If you need practice, avoid using them, or you might run out of self-assessment problems. Problems Exercise 1 Prove or disprove ∀x ∈ R, ∃y ∈ R : x − y3 = 0 Exercise 2 Prove or disprove ∃y ∈ R, ∀x ∈ R : x − y3 = 0 Exercise 3 Prove or disprove ∀x ∈ N, ∃y ∈ N : x − y3 = 0 Exercise 4 Prove or disprove ∃y ∈ N, ∀x ∈ N : x − y3 = 0