Activity 1.1.2: Truth Tables and Deduction p = "You used the pool in the afternoon." q = "You cleaned up after lunch." r = "You must clean up after dinner." 1. Use connectives to translate the following statement into formal logic. o If you used the pool in the afternoon and you didn't clean up after lunch, then you must clean up after dinner. 2. Construct a truth table for the formal logic statement that you found in part (1). The eight rows of your table should correspond to the eight different possibilities for p, q, and r. (See the last activity for an example.) 3. Suppose that the statement given in part (1) is false. What must be true about your pool usage and cleanup duties? Explain how to justify your answer using the truth table. Activity 1.2.1: Using Equivalence Rules In Activity 2 of last section, you translated the statement "If you used the pool in the afternoon and you didn't clean up after lunch, then you must clean up after dinner" into formal logic using the following variables. p = "You used the pool in the afternoon." q = "You cleaned up after lunch." r = "You must clean up after dinner." 1. Use the implication rule to rewrite your formal logic statement so that it doesn't contain the connective. 2. Use De Morgan's laws to rewrite the resulting statement from part (1) so that it doesn't contain the connective. 3. Use equivalence rules to simplify the negation of your statement from part (2) so that it doesn't use parentheses. 4. Without using truth tables, can you give an alternative explanation for your conclusion in part (3) of Activity 1.1.2?