2. Venn Diagrams Truth Sets & Valid Arguments Truth Sets & Valid Arguments Truth Tables Implications Truth Tables Implications Truth Tables Converse, Inverse, CP 50 40 30 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

3. State the inverse: If I do my homework, then I have an A on the test.

4. State the contrapositive: If it is snowing, then we will not have school.

5. P: I like cheese Q: I like pizza. Write the following in symbols: If I do not like pizza, then I do not like cheese.

6. Prove that the converse and inverse are logically equivalent.

7. Prove that the implication and the contrapositive are logically equivalent.

8. Create a truth table for ~ p Λ ~ q

9. Create a truth table for (p V q) Λ q

10. Create a truth table for ~ (p V q) Λ q

11. Create a truth table for ~ (p V q) V ~ q

12. Determine if the following are logically equivalent: ~(p Λ q) = ~p V ~q

13. Construct a truth table for the following ~ (p ↔ q )

14. Determine if the following are tautologies, logical contradictions, or neither. ( p V q) → ( ~p)

15. Determine if the following are tautologies, logical contradictions, or neither. (p Λ q) → (p V q)

16. Determine if the following are tautologies, logical contradictions, or neither. p Λ (p ↔ q)

17. Determine if the following are tautologies, logical contradictions, or neither. (p → ~q) V (~p → q)

18. List the truth sets for U, P, and P’ U = { x ⃓ 0 < x ≤ 18, x є N} p: the set of prime numbers

19. List the truth sets and draw a diagram U = { x ⃓ 0 < x ≤ 20, x є N} p: even numbers q: prime numbers

20. Determine the validity of the argument

23. Represent the following on a Venn Diagram p Λ q

24. Represent the following on a Venn Diagram ~p V ~q

25. Express in terms of P and Q

26. Express in terms of p and q

27. Represent using a Venn Diagram q V (p Λ r)