Define the following propositions: j: Sally got the job. l: Sally was late for her interview r: Sally updated her resume. Express each pair of sentences using logical expressions. Then prove whether the two expressions are logically equivalent. (a) If Sally did not get the job, then she was late for her interview or did not update her resume. If Sally updated her resume and did not get the job, then she was late for her interview. (b) If Sally did not get the job, then she was late for her interview or did not update her resume. If Sally updated her resume and was not late for her interview, then she got the job. (c) If Sally got the job then she was not late for her interview. If Sally did not get the job, then she was late for her interview. (d) If Sally updated her resume or she was not late for her interview, then she got the job. If Sally got the job, then she updated her resume and was not late for her interview.