Drawing a Truth Tree for Propositional Logic Argument

I want solutions to the questions I am attaching below.

Competencies 5 & 6

Is the following argument valid? Draw a truth table to show whether it is valid or not; if it is invalid, give a counterexample:

((P & Q) v (Q ≡ R)), (¬P v R) Therefore (¬Q É R)

Competency 7

Draw a truth-tree for the following propositional logic argument. Give a counterexample if it is invalid.

(P v (¬S > Q)), (P > R) Therefore (¬(Q & R) > S)

Competency 8

Prove the following derivation using Natural Deduction. For this example, you will not need to use assumptions; you are permitted to, however, so long as you use them correctly.

((¬ Q > P) v Q), (¬ Q v R), (¬R & S) Therefore (P v ¬S)

Competency 9

Prove the following derivation using Natural Deduction. For this example, you WILL need to use at least one assumption.

((¬ P v R) > Q), (S ≡ (Q v P)) Therefore (¬P > S)

Competency 14 and 15

Using a truth-tree, test the following predicate logic (QL) argument for validity. If it is invalid, construct a valuation that shows this.

Ex(Px & Hx), Ax(Gx É Hx) Therefore (ExGx > AxHx)