(Solved): Problems: (a) 'Exclusive or'-written \( \oplus \) - is the logical connective with truth table Fin ...

Problems: (a) 'Exclusive or'-written \( \oplus \) - is the logical connective with truth table Find an expression in \( P \) and \( Q \), using only the connectives \( \wedge, \vee \) and \( \sim \), that is equivalent to \( P \oplus Q \). (b) Which of the following statements are tautologies? (1) \( ((P \Rightarrow Q) \vee(Q \Rightarrow P)) \Rightarrow Q \) (2) \( ((P \Rightarrow Q) \wedge(P \Rightarrow(\sim Q))) \Rightarrow(\sim P) \) (3) \( (P \wedge Q) \vee((\sim P) \wedge Q) \vee(\sim Q) \) (4) \( ((P \Rightarrow Q) \wedge(Q \Rightarrow R)) \Rightarrow(P \Rightarrow R) \)