Written without proper operators since upload error when using them. ( and = conjunction, negation = not operator)

Please make sure you include the name of the rule for every step!

1. a) Using only the Negation and conjunction operators, find a logical expression that is equivalent to "p <-->(Negation q V r)". Prove that the expression you found is equivalent by using logical equivalences (state their names next to the line they were applied in).

b) Prove that the expression you found for a) above is equivalent to "p <--> (Negation q V r)" by using truth tables. Show all your work (i.e., ensure you that you include a new column for every single operation).

2. Determine if the following expressions are tautologies, contradictions, or contingencies by using logical equivalences. Show all your work..

a)Negation(Negation p And p) V q"

b. (p --> p) And Negation(q <--> q)