1. Determine whether the following arguments are valid or invalid. If they are valid, then state the rules of inference used to prove validity. If they are invalid, outline precisely (3 marks each) why they are in valid. a. Ifit is snowing then I do not wear shorts to work. I did not wear shorts to work. Therefore, it must be snowing b. Everyone taking COMP1501 next semester plays computer games. Therefore, everyone who plays computer games must be taking COMP1501 next semester, At least one person has been to the moon. Anyone that has been to the moon had to travel through space. Everyone who has travelled through space has experienced microgravity. Therefore, at least one person has experienced microgravity c. 2. Prove, by indirect proof, that if n is an integer and n3 + 3 is odd, then n is even. Show (5 marks) all vour work. Prove or disprove that x4-4x3-2x2 + 12x-4 is a negative value for every integer (5 marks) 3. in the range -1