1. Determine whether the following argument is valid or invalid. If it is valid, then yoiu must state the rules of inference used to prove validity, but if it is not then you must provide an example to outline precisely why it is invalid. [nb., You do not need (4 marks) quantified predicate logic expressions to complete this problem.) "IfI am a student in computer science then I have access to a computer and I enjoy playing computer games. IfI have access to the computer labs then I have access to a computer. I have access to the computer labs and I enjoy playing computer games. Therefore, I am a student in computer science." 2. Starting from the four numbered premises below (which are assumed to be true) and using only the rules of inference (including the instantiation and generalization rules) and the logical equivalences (as both were presented in class), show that 3x E(x) Make sure that you include both the rule and the line number(s) to which that rule is applied (6 marks) 2) 3x C(x) A(x) 3) Vx -C(x) - D(x) 4) vx D (x) E (x) 3. Prove, by indirect proof, that if n is an integer and 3n + 1 is even, then n is odd. Show (4 marks) all vour work. 1. Determine whether the following argument is valid or invalid. If it is valid, then yoiu must state the rules of inference used to prove validity, but if it is not then you must provide an example to outline precisely why it is invalid. [nb., You do not need (4 marks) quantified predicate logic expressions to complete this problem.) "IfI am a student in computer science then I have access to a computer and I enjoy playing computer games. IfI have access to the computer labs then I have access to a computer. I have access to the computer labs and I enjoy playing computer games. Therefore, I am a student in computer science." 2. Starting from the four numbered premises below (which are assumed to be true) and using only the rules of inference (including the instantiation and generalization rules) and the logical equivalences (as both were presented in class), show that 3x E(x) Make sure that you include both the rule and the line number(s) to which that rule is applied (6 marks) 2) 3x C(x) A(x) 3) Vx -C(x) - D(x) 4) vx D (x) E (x) 3. Prove, by indirect proof, that if n is an integer and 3n + 1 is even, then n is odd. Show (4 marks) all vour work