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Running
on
Zero
1.3 No 64
#88
by
fauyiyuji67
- opened
๐: Construct a compound proposition that asserts that ev ery cell of a 9 ร9 Sudoku puzzle contains at least one number
๐ค: Here is a possible compound proposition for the statement you provided:
Let C be a 9 x 9 Sudoku puzzle. Then, every cell c in C satisfies the following condition: there exists a unique integer value v such that v appears exactly once in each row, column, and 3x3 sub-grid of c.
To break this down into simpler propositions, we can use the following definitions:
- For any given cell c in C, let R(c) denote the set of rows containing c.
- For any given cell c in C, let C(c) denotes the set of columns containing c.
- For any given cell c in C, let S(c) denotes the set of 3x3 sub-grids containing c.
Then, our compound proposition becomes:
For all cells c in C, there exists a unique integer value v such that:
- v appears exactly once in each row of R(c).
- v appears exactly once in each column of C(c).
- v appears exactly once in each 3x3 sub-grid of S(c).
This proposition asserts that every cell in the Sudoku puzzle has at least one number assigned to it.