1.3 No 64

#88
by fauyiyuji67 - opened

๐Ÿ˜ƒ: Construct a compound proposition that asserts that ev ery cell of a 9 ร—9 Sudoku puzzle contains at least one number
๐Ÿค–: 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:

  1. v appears exactly once in each row of R(c).
  2. v appears exactly once in each column of C(c).
  3. 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.

Sign up or log in to comment