Maths · Relations, type of relations, equivalence relations

Which of the following statements is the contrapositive of the statement, You wi

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

  • A. If you lose the game then you dont know the rules or you are overconfident
  • B. A sufficient condition that you win the game is that you know the rules or you are not overconfident
  • C. If you dont know the rules or are overconfident you lose the game
  • D. If you know the rules and are overconfident then you win the game

Step-by-step solution

The original statement 'You win the game if you know the rules but are not overconfident' can be rewritten as 'If (you know the rules and are not overconfident), then (you win the game)'. The contrapositive of 'If P then Q' is 'If not Q then not P'. Here, P = 'know the rules and not overconfident', Q = 'win the game'. Not Q is 'lose the game'. Not P is 'not (know the rules and not overconfident)', which by De Morgan's law is 'do not know the rules or are overconfident'. Thus, the contrapositive is 'If you lose the game, then you do not know the rules or you are overconfident', which matches option A.
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