Explain the meaning of the following expression: A → (B, C) Given this expression, tell if it is also true that: A → B and: A → C

:Given the pair of statements: A →~Z and Z=[Av (A•~Z)] 20. Construct a complete (ordinary) truth table for relation between the above pair of statements 21. How are the statements A-Z and Z = [A V (A • ~Z)] related? Given the argument: ~Av (B = C) B⇒ ~A ~A B Therefore, A. ~C 22. Construct a complete (ordinary) truth table. 23. Test for validity

Mathematical Logic. First-order or predicate logic. For each of the following relations, give a formula that defines it in (N;+,∙). The language has equality and has the parameters ∀,+ and ∙. a) {0} b) {1} c) {〈m,n〉| n is the successor of m in N} d) {〈m,n〉| n<n in N} Please be as clear as possible. Thank you.

The teams is a sports competition are divided into six groups with five teams in each group. Each team plays the other teams in its group once only. Write a Prolog preciate schedule(S) that is true if S is a valid schedule. A schedule lists the fixtures for each day of the competition. In a fixture (A,B), team A is the home team and team B is the away team. A schedule is valid if: • there are no more than three matches on any day, • each team has the same number of home and away fixtures in the whole schedule, and • each team has at least four rest days between fixtures. Ideally the schedule S should be as short as possible, and the predicate schedule should be able to generate multiple valid schedules.