Question 1: Determine whether the following propositions are True [T] or False [F]. If False, provide a clear counterexample. 1) "Some valid arguments have false conclusions." 2) "Some invalid arguments have false conclusions." 3) "If an argument has all the premises and the conclusion true, it must be valid." 4) "All valid arguments preserve truth." 5) "All invalid arguments preserve falsity." Question 2: Compute the truth values of the following propositions, given that A,B, and C are true, and X,Y, and Z are false. 1) (AB)(XY) 2) B(X&Y) 3) ((A&X)B) 4) (AZ)(CY) 5) (A(X(B(Y(CZ))))) Question 3: Given that A,B, and C are true, X,Y, and Z are false, and without being given the truth values of G and H, can you figure out the truth values of the following? If yes, what are they? (I.e., for each formula, state whether it is True [T], False [F], or Not enough information to decide whether it's true or false [N]) 1) (AG)&(BH) 2) (A&G)(B&H) 3) (XG) 4) H(HG) 5) (HG)(AB) Question 4: Use any truth-table method (the full truth-table method or the partial truth-table method) to determine whether the following argument forms are valid or invalid. 1)(pq)3)(p&q)(pq)p(p&q)qp(pq)(p&q)qp 2)(pq)q&p4)q(p&r)r(pq)(qp)r(qp)r(p(p&q))(pr)