{"id":1080,"date":"2017-01-11T00:44:03","date_gmt":"2017-01-11T00:44:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&p=1080"},"modified":"2017-04-04T23:08:35","modified_gmt":"2017-04-04T23:08:35","slug":"why-it-matters-set-theory","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/why-it-matters-set-theory\/","title":{"raw":"Why It Matters: Set Theory and Logic","rendered":"Why It Matters: Set Theory and Logic"},"content":{"raw":"

Let\u2019s play a game!<\/h2>\r\n \r\n\r\n\"Tic-Tac-Toe<\/a>Almost everyone knows the game of Tic-Tac-Toe, in which players mark X\u2019s and O\u2019s on a three-by-three grid until one player makes three in a row, or the grid gets filled up with no winner (a draw). \u00a0The rules are so simple that kids as young as 3 or 4 can get the idea.\r\n\r\n \r\n\r\nAt first, a young child may play haphazardly, marking the grid without thinking about how the other player might respond. \u00a0For example, the child might eagerly make two in a row but fail to see that his older sister will be able to complete three in a row on her next turn.\r\n\r\n \r\n\r\nIt\u2019s not until about age 6 or so that children begin to strategize, looking at their opponent\u2019s potential moves and responses. \u00a0The child begins to use systematic reasoning, or what we call logic, to decide what will happen in the game if one move is chosen over another.\r\n\r\n \r\n\r\n \r\n\r\nThe logic involved can be fairly complex, especially for a young child. \u00a0For example, suppose it\u2019s your turn (X\u2019s), and the grid currently looks like this. \u00a0Where should you play?\r\n\r\n\"Tic-tac-toe<\/a>\r\n\r\n \r\n\r\nYour thought process (or what we call a logical argument) might go something like this:\r\n