Specification for Assignment 1014 4. Using only the and the A operators, find a logical expression that is equivalent to (p Vr) - -. For this question, you do not need to specify "how" you found the equivalent expression because you will show both techniques in questions 5 and 6 below. (0.5 marks) 5. Prove that the expression you found for question 4 above is equivalent to the expression (p V r ) by using only truth tables. Show all your work and do not skip any steps (i.e., ensure you that you include a new column for every single operation) (4.0 marks) Prove that the expression you found for question 4 above is equivalent to the expression (p V - by using only the logical equivalences. Show all your work and do not skip any steps. (4.0 marks) 7. Determine if the following expressions are tautologies, contradictions, or contingencies by using truth tables. Show all your work. (10.0 marks) a. (pvq) v (p - 9) b. (p ) () c. ((q --p) (q^p)) - ( p p) . 8. Determine if the following expression is a tautology, a contradiction, or a contingency by using the logical equivalences. You may not use a truth table. Show all your work, labelling each rule used, and do not skip any steps. (4 marks) a. (a - b Vc)) ^ (Gb-c) Aa)