Explain each problem in full detail but keep it simple

Please show your work on all problems unless specific instructions state otherwise. If work is required to obtain an answer, that work must be shown on this paper in order to receive credit. If extra space is needed, please show as much work as possible on the test and then note "see paper" to indicate that work continues on the extra sheets provided. Partial credit can only be given in cases where work demonstrates knowledge and understanding worthy of such credit. Please give exact numerical answers when possible. When requested, round answers to three decimal places unless you are otherwise instructed. 1. Assume that the following implication is true. Use the implication to answer parts a through c. If it is raining, then Sam will be carrying an umbrella a) If it is not raining can we conclude that Sam will not be carrying an umbrella? Please explain. This Implication troc to cause sam ceas not b) Write the contrapositive of the statement below. mtrolla A raining TITIT c) Circle the statements below that are logically equivalent to the implication statement. To be raining is a necessary condition for Sam to be carrying an umbrella ii ) Sam carrying an umbrella is a necessary condition for it to be raining 10 1 - cord iii) book If Sam is carrying an umbrella then it is raining iv ) To be raining is a sufficient condition for Sam to carry an umbrella V ) It is raining only if Sam is carrying an umbrella 2. Let P(x) be the predicate, "5x +1" is prime. a) Is the value P(2) true or false? b) Is the value P(5) true or false? c) Is Vx P(x) true or false? d) Is Ax P(x) true or false