Please answer all the questions in the photo. Don't SKIP. Thank you!

1. Construct a truth table for the statement (circle your final answer): (pq)(qp) 2. If p,q and r are all false, find the truth value of the statement: (show your work/justify your answer). [p(qr)]p 3. a) Use the given simple statements p,q and r to write the statement below in symbolic form. b) Determine the truth value of each simple statement p,q and r. Then, use those truth values to determine the truth value of the compound statement. (Show your work/justify your answer) p: Three plus five equals five plus three. q: Tiger Woods is President of the United States. r : Fall River is the capitol of Masachusetts. "If three plus five equals five plus three and Tiger Woods is not President of the United States, then Fall River is the capitol of Massachusetts." 4. Use DeMorgan's law to write an equivalent statement for each (your final answer should be in words). a) "It is false that the Patriots game is on TV and I am not watching it." b) "The price is below $5000 or I will not buy the car." 5. Use the fact that pq is equivalent to pq to write an equivalent statement for each (answer in words). a) "The price is below $5000 or I will not buy the car." b) "If it rains, then I will not mow the lawn." 6. Write the converse, inverse and contrapositive of each statement (your final answers should be in words). a) "If the dog is a pit bull, then the neighbors are not safe." b) Which, if any, of the 3 answers to part (a) are logically equivalent to each other? 7. Determine which, if any, of the 3 statements, a, b, or c, are equivalent to each other. Show your work/justification. For justification, you may use truth tables, or any of the laws we know to be true. a) A baseball player does not use steroids or he is likely to have physical breakdowns. b) If a baseball player is not likely to have physical breakdowns, then he does not use steroids. c) It is false that a baseball player does not have physical breakdowns and he uses steroids