On April 20, 2017, John and Mary sign the following contract: - If it rains on May 1, 2017, then John must give Mary a check for $10,000 on May 2, 2017 - If John gives Mary a check for $10,000 on May 2, 2017, Mary must mow the lawn on May 3, 2017. What truly happened those days is the following: - it did not rain on May 1, 2017 - John gave Mary a check for $10,000 on May 2, 2017 - Mary mowed the lawn on May 3, 2017. Part a: Write a first order logic statement to express the contract. Make sure that you clearly define what constants and predicates that you use are. (NOTE: DO NOT use functions) Part b: Write a logical statement to express what truly happened. When possible, use the same predicates and constants as in question 6a. If you need to define any new predicates or constants, clearly define what they stand for. Part c: Was the contract violated or not, Justify your answer Part d (10 pts EC for 4308, req for 5360): Define the symbols required to convert any KB involved in the above domanin from FOL to Propositional logic. Use this to convert the answers to part a and b to Propositional Logic.