Can you be clear on the explanation please. Thank you in advance.

1. (10 points) Rewrite the statement in the if-then form in two ways, one of which is the contrapositive of the other. This quadratic equation has two distinct real roots if, and only if, its discriminant is greater than zero. 2. (20 points) Use truth tables to establish the truth of the statement. A conditional statement is not logically equivalent to its inverse. 3. (20 points) Construct a truth table for the statement form in (pq)p. 4. (20 points) Use truth tables to verify the following logical equivalences. Include a few words of explanation with your answers. (pq)r(pr)(qr) 5. (14 points) Write contrapositives, converse, and inverse for the statement (write the formula with your answer). If today is Easter, then tomorrow is Monday. 6. (16 points) Let E={1,2,3} and F={2,1,0} and define a relation T from E to F as follows: For all (x,y)EF,(x,y)T means that 3xy is an integer. a. Is 3TO ? Is 1T(1) ? Is (2,1)T ? Is (3,2)T ? b. Write T as a set of ordered pairs. c. Write the domain and co-domain of T. d. Draw an arrow diagram for T