1.1: The negation of \( (P \wedge(Q \rightarrow R)) \) is a) \( \neg(P \wedge Q) \rightarrow \neg R \) d) \( \neg P \vee Q \vee R \) b) \( \neg R \rightarrow(P \wedge Q) \) e) None of the above c) \( P \vee(Q \wedge \neg R) \) 1.2: The first four terms of an arithmetic sequence are \( 3,8,13 \), and 18 . What is the \( n \)th formula of the sequence for \( =0,1,2, \ldots \). a) \( a_{n}=5 n+3 \) d) \( a_{n}=5 n+2 \) b) \( a_{n}=5 n-2 \) e) None of the above c) \( a_{n}=5 n+8 \) 1.3: The binary representation of \( (9 A 3)_{16} \) is a) 100110100011 d) 111010100011 b) 110110100011 e) None of the above c) 100101110011 1.4: If \( a \equiv 5(\bmod 9) \), then a may equal to a) 16 d) 41 b). 22 e) None of the above c) 30 1.5: The incidence matrix for a graph with 5 vertices and 7 edges has \( \qquad \) rows and \( \qquad \) columns. a) 5 rows and 7 columns d) 7 rows and 7 columns b) 6 rows and 12 columns e) None of the above c) 5 rows and 5 columns Each question is worth 10 marks. Answer the following questions: Q-2: a) [5 marks] Construct the truth table of the statement: \( \neg(p \wedge q) \rightarrow(q \wedge \neg p) \). Determine whether the statement is a tautology. b) [2 marks] Consider the predicate \( P(x, y, z) \) consists of triples \( x, y, z \) where \( x= \) \( \{0,1\}, y=\{1,2\} \), and \( z=\{0,1\} \). Write out the proposition \( \forall x P(x, 1,1) \) using conjunctions and disjunctions. c) \( [2+1 \) marks] Let \( A=\{0,1,3,4\} \) and \( B=\{1,2,4\} \). Find i. \( (A \cap B) \times B \), ii. \( P(B) \).