Why It Matters: Set Theory and Logic
Why understand set theory and logic applications?
Almost everyone knows the game of Tic-Tac-Toe, in which players mark X’s and O’s 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). The rules are so simple that kids as young as 3 or 4 can get the idea. At first, a young child may play haphazardly, marking the grid without thinking about how the other player might respond. For 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. It’s not until about age 6 or so that children begin to strategize, looking at their opponent’s potential moves and responses. The 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. The logic involved can be fairly complex, especially for a young child. For example, suppose it’s your turn (X’s), and the grid currently looks like this. Where should you play? Your thought process (or what we call a logical argument) might go something like this:- It takes three in a row to win the game.
- I cannot make three in a row no matter where I play on this turn.
- If it were my opponent’s turn, then she could make three in a row by putting an O in the upper left corner.
- If I don’t put my X in the upper left corner, then my opponent will have the opportunity to play there.
- Therefore, I must put an X in the upper left corner.
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CC licensed content, Original
- Why It Matters: Set Theory and Logic. Authored by: Lumen Learning. License: CC BY: Attribution.
- Tic Tac Toe game example. Authored by: Lumen Learning. License: CC BY: Attribution.
- Tic Tac Toe example play. Authored by: Lumen Learning. License: CC BY: Attribution.
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- Tic Tac Toe playground game. License: CC0: No Rights Reserved.