need help on dicrete structure please 1. Consider the following variant of the g

Question

need help on dicrete structure please

1. Consider the following variant of the game Nim. The board with 10 pebbles on a board, and the two players take turns removing either 2 or 3 pebbles. The first player who is unable to remove any pebbles from the board (e.g., there are only 1 or O pebbles left) is the loser. Represent this game using propositional logic. Be sure to describe the representation i.e., how propositions represent the current state of the board), the initial configuration, any constraints on the representation (e.g., there can't be both 4 and 7 pebbles on the board at the same time), how the game evolves (e.g., how to the players play and take turns), and a condition that player 1 win:s 2. Recast your solution to problem 1 into predicate logic.

Explanation / Answer

Solution:

1) A and B are two players Only one at time can remove 2 or 3 pebbles and there exist (is) a situation where one of player remains 0 or 1 pebble is the losser

note such situation exist because we have finitely many i,e 10 pebbles

and CONDITION that player 1 win is that take pebble so that remaining no of pebbles is after division remainder is 2 or 3

2) so we have predicate logic for proposition : A and B are two players Only one at time can remove 2 or 3 pebbles and there exist (is) a situation where one of player remains 0 or 1 pebble is the losser is being that player 1 win is that take pebble so that remaining no of pebbles is after division remainder is 2 or 3

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