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Consider the following universal affirmative statement: "All games involve a winner and a loser." What is a counterexample to this statement?

a) Games without any winner or loser
b) Games with multiple winners
c) Games with a single participant
d) Games with only a loser

1 Answer

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Final answer:

A counterexample to the statement "All games involve a winner and a loser" is games without any winner or loser, such as cooperative games where players work together and either win or lose as a group.

Step-by-step explanation:

To consider the universal affirmative statement - "All games involve a winner and a loser", we need to find a counterexample that contradicts this statement. A counterexample to this statement would be option a) Games without any winner or loser. An example of such a game could be a cooperative board game where all players work together towards a common goal, and they either all win or lose together, effectively having no individual winner or loser.

Counterexamples are crucial in disproving universal statements, as a single instance where the statement does not hold is sufficient to show that the statement is not universally true. This demonstrates the concept of necessity and sufficiency in logical relations, where finding a single instance that does not meet the necessary conditions or doesn't lead to a sufficiency is enough to refute a universal claim.

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