2. If then Therefore It is rainingthe ground is wet It is raining the ground is wet

3. If then Therefore

4. If then Therefore you are a fish you can swim

5. If then Therefore you are a fish you can swim This argument structure is invalid because the premises do not force you to believe the conclusion. While it is possible that all of these statements are true ( I might be talking to a fish ) my reasoning is not valid because it is also possible that the premises are true and the conclusion is false ( I am talking to a person who can swim.) There are conditions under which the premises are true and the conclusion is false.

6. When we analyze an argument to determine whether its structure is valid or invalid, we are not concerned with whether the statements are true or false but rather the conditions under which each statement is true or false. To accomplish this we will build a truth table.

7. AND Fish swim and birds fly. Fish swim and cows fly. Cows fly and fish swim. Cows fly and fish tap dance. T T T T F F FF

8. Under what conditions is an “AND” statement true ? Only when both components are true

9. OR Bananas can be yellow or bananas can be green. Tangerines are orange or tangerines are purple. Oranges are blue or oranges are orange. Apples are blue or apples are lavender. T T T T F F FF

10. Under what conditions is an “OR” statement false ? Only when both components are FALSE

11. IF … THEN “If John studies then he will pass.” Under what conditions am I lying? Consider the possibilities.

12. IF … THEN “If John studies then he will pass.” Under what conditions am I lying? Consider the possibilities. Blue true green false

13. Under what conditions is an “IF … THEN” statement false ? Only when “if” component is true and “then” component is false

14. The NEGATION of a true statement is false. One plus one equals two. o is true One plus one does NOT equal two. ~ o is false I am Miss America. m is false I am NOT Miss America. ~m is true The NEGATION of a false statement is true.

16. IF AND ONLY IF John is happy if and only if he is studying means John is happy if he is studying AND John is happy only if he is studying

17. s  h

20. h if and only if s is true when both components have same truth value s  h

21. Build a truth table for the statement:

22. Locate the dominant connective Now we have two easier statements to deal with

26. Build a truth table for the statement: