1.3 No 65

#90
by rgwfwerfwqedqwed - opened

😃: Explain the steps in the construction of the compound proposition given in the text that asserts that every col umn of a 9×9Sudoku puzzle contains every number.
🤖: The construction of the compound proposition for Sudoku involves breaking down the problem into smaller parts and using logical reasoning to arrive at the conclusion that every column of a 9x9 Sudoku puzzle contains every number from 1 to 9. Here are the steps involved:

Step 1: Identify the columns of the Sudoku grid. In this case, there are 9 columns, labeled A through I.

Step 2: Define each column as a set of cells, where each cell represents one position in the column. For example, Column A consists of the cells A1-A9, B1-B9, etc.

Step 3: Use the following claim to break down each column into smaller sub-sets:

Claim: Every row of the Sudoku grid contains exactly one copy of each number from 1 to 9.

Proof: By assumption, every row of the Sudoku grid contains only one instance of each number from 1 to 9. Therefore, any subset of rows (i.e., a single column) must...

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