MATHEMATICS in the MODERN WORLD Name: Date: Course & Section: Rating: EXERCISES: NO. 21 A. Use an Euler Diagram to determine whether or not the following is valid. 1. All fish eat algae. Nemo does not eat algae. Therefore, Nemo is not a fish. 2. No snake is a mammal. All horses are mammals. Therefore, no fish is a cow.MATHEMATICS in the MODERN WORLD ~r) + q) Name: Date: Course & Section: Rating: EXERCISES: NO.20 A. Formalize the following sentences: A. Consider a propositional language where: p means "Red is happy", . q means "Red dances gracefully", . r means "Izy is happy". 1. If Red is happy then he dances gracefully. 2. Red is happy and Izy is also happy. 3. If Red is happy and dances gracefully then Izy isn't happy. B. Consider a propositional language where: P = Princess comes to the party. g = Grace comes to the party. 1 = Leslie comes to the party. S = Shiela comes to the party.Section 2 | MATHEMATICS AS A TOOL 4. If Leslie comes to the party then Princess comes too. 5. If Princess comes to the party then Grace and Shiela come too. 6. Shiela comes to the party if and only if Leslie comes and Princess doesn't come. 7. Grace comes to the party only if Princess and Leslie do not come. 8. Grace and Shiela come to the party. 9. Either Leslie comes to the party or Princess doesn't come. 10. Princess, Grace and Leslie come to the party if and only if Shiela doesn't come