Logic Homework #2 Due Wed. 2/27Instructions: Translate the ten examples below from English into the symbolic language of SL. You will make a symbolization key designating a capital letter for each sentence that you translate and you will also use the 5 logical connectives that we have studied in class. Some of these examples are individual sentences and others are arguments. If the example is of an argument then translate it in standard form with each premise on a separate line divided from the conclusion by a horizontal line. Each of the problems is worth ten points. 1) If Joan Davis wins the Oscar then Betty Davis will cry. If Betty Davis cries then Elizabeth Taylor will take pity on her. Elizabeth Taylor won’t take pity on Betty Davis. So, Joan Crawford will not win the Oscar. 2) Charlotte and Emily Bronte are happy and Joan Crawford has no siblings. 3) If Hilary wins the presidential election then neither she nor Bill will return to New York.4) Neither Trump nor Rubio will get the Republican nomination but both of them want to be the next president. 5) Worf will regain his family honor only if Sisko befriends the Romulans and the Federation defeats the dominion. 6) Clinton will be the next president unless Sanders wins the California primary in which case he will be the next president. 7) If Worf fires the photon torpedoes then the Borg will be destroyed unless the Dominion comes to their aid and the Romulans attack the federation.8) Athos will rescue the king and Porthos will unmask the cardinal if but only if Aramis captures the treacherous duchess. 9) The Cardinal will usurp the throne and behead the king only if Aramis, Athos, and Porthos drink too much wine. 10) Athos will be locked in the Bastille if the Cardinal usurps the throne. Athos will not be locked in the Bastille unless Porthos is arrested for public intoxication. Porthos won’t be arrested for public intoxication, so the Cardinal will not usurp the throne.