Transcription of Math 55: Discrete Mathematics
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Math 55: Discrete Mathematics
math 55: Discrete MathematicsUC Berkeley, Fall 2011 Homework # 1, due Wedneday, January the propositions The election is decided and Thevotes have been counted, respectively. Express each of these compoundpropositions as English ) p: The election is not (yet) )p q: The election is decided or the votes have been ) p q: The votes have been counted but the election is not (yet) )q p: If the votes are counted then the election is ) q p: The election is not decided unless the votes havebeen ) p q: The votes have not been counted unless the electionhas been decided. This is equivalent to proposition d).g)p q: The election is decided if and only if the votes have ) q ( p q) : The votes have not been counted, or they havebeen counted but the election is not (yet) whether each of these conditional statements is true )If1 + 1 = 3, then unicorns statement is true becauseF Fhas the truth )If1 + 1 = 3, then dogs can statement is true becauseF Fhas the truth )If1 + 1 + 2, then dogs can statement is false becauseT Fhas the truth )If2 + 2 + 4, then1 + 2 = statement is true becauseT Thas the truth each of these propositions in the form pif and only ifq )For you to get anAin this course, it is necessary and suf
icates, quanti ers and logical connectives. Let C(x) denote the predi-cate \x is in the correct place", let E(x) denote the predicate \x is in excellent condition", and let T(x) denote the predicate \x is a tool". and suppose that the domain consists of all tools. a) Something is not in the correct place. 9x :C(x).
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