Let p, q and r be the propositions p: you get a recommendatio you work hard. r: you get promoted. n on the end of the year. q Write the following propositions using p, q, and r and logical connectives (a) You got promoted, but you do not work hard. (b) You get a recommendation on the end of the year, you work hard, and get promoted. (c) To get promoted, it is necessary for you to get a recommendation at the end of the year. (d) You get a recommendation on the end of the year, but you don't work hard; nevertheless, you get promoted. (e) Getting a recommendation on the end of the year and working hard is sufficient for getting promoted. the end of the year