{"id":1918,"date":"2017-03-20T03:05:18","date_gmt":"2017-03-20T03:05:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&p=1918"},"modified":"2020-04-22T22:33:47","modified_gmt":"2020-04-22T22:33:47","slug":"introduction-introduction-to-logic","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/introduction-introduction-to-logic\/","title":{"raw":"Introduction to Logic Basics","rendered":"Introduction to Logic Basics"},"content":{"raw":"

What you\u2019ll learn to do: Create truth tables to interpret statements and conditionals<\/h2>\r\nIn this section, we will learn how to construct logical statements. We will later combine our knowledge of sets with what we will learn about constructing logical statements to analyze arguments with logic.\r\n\r\nLogic is a systematic way of thinking that allows us to deduce new information\u00a0from old information and to parse the meanings of sentences.\u00a0You use logic informally in everyday life and certainly also in doing mathematics.\u00a0For example, suppose you are working with a certain circle, call it\u00a0\u201cCircle X,\u201d and you have available the following two pieces of information.\r\n
    \r\n \t
  1. Circle X has radius equal to 3.<\/li>\r\n \t
  2. If any circle has radius [latex]r[\/latex], then its area is [latex]\\pi{r}^{2}[\/latex]\u00a0square units.<\/li>\r\n<\/ol>\r\nYou have no trouble putting these two facts together to get:\r\n
      \r\n \t
    1. Circle X has area [latex]9\\pi[\/latex] square units.<\/li>\r\n<\/ol>\r\nYou are using logic to combine existing information to\u00a0produce new information. Since a major objective in mathematics is to\u00a0deduce new information, logic must play a fundamental role. This chapter\u00a0is intended to give you a sufficient mastery of logic.\r\n\r\n ","rendered":"

      What you\u2019ll learn to do: Create truth tables to interpret statements and conditionals<\/h2>\n

      In this section, we will learn how to construct logical statements. We will later combine our knowledge of sets with what we will learn about constructing logical statements to analyze arguments with logic.<\/p>\n

      Logic is a systematic way of thinking that allows us to deduce new information\u00a0from old information and to parse the meanings of sentences.\u00a0You use logic informally in everyday life and certainly also in doing mathematics.\u00a0For example, suppose you are working with a certain circle, call it\u00a0\u201cCircle X,\u201d and you have available the following two pieces of information.<\/p>\n

        \n
      1. Circle X has radius equal to 3.<\/li>\n
      2. If any circle has radius [latex]r[\/latex], then its area is [latex]\\pi{r}^{2}[\/latex]\u00a0square units.<\/li>\n<\/ol>\n

        You have no trouble putting these two facts together to get:<\/p>\n

          \n
        1. Circle X has area [latex]9\\pi[\/latex] square units.<\/li>\n<\/ol>\n

          You are using logic to combine existing information to\u00a0produce new information. Since a major objective in mathematics is to\u00a0deduce new information, logic must play a fundamental role. This chapter\u00a0is intended to give you a sufficient mastery of logic.<\/p>\n

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          Candela Citations<\/h3>\n\t\t\t\t\t
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          CC licensed content, Original<\/div>