Question

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 don’t 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 don’t know the rules or are overconfident you lose the game.
D. If you know the rules and are overconfident then you win the game

Answer 1

Hint:When two statements are presented, then Contrapositive means switching the hypothesis and conclusion of a conditional statement and negating both whereas Inverse means negating both the statements, and converse means reversal of both the statements.

Complete step by step answer:
In the given question we have to look for the contrapositive.To make it simple we can see an example like as,
Statement: if ‘p’, then ‘q’.
Converse: if ‘q’, then ‘q’.
Inverse: if not ‘p’, then not ‘q’.
Contrapositive: if not ‘q’, then not ‘p’.
Contrapositive is actually the inverse of the converse of the statement. It is attained by first interchanging the hypothesis and conclusion and then adding "not" to both (negating both).In this case, the converse is "If you win the game, then you know the rules but are not overconfident."

Inverse of this statement gives an answer. Here in the given question,
statement, “You win the game if you know the rules but are not over confident?"
Converse: if you know the rules and are not overconfident you will win the game
Inverse: you will not win the game if you don’t know the rules or are overconfident
Contrapositive: If you don't know the rules or are overconfident you lose the game.
Here ‘q’ is – if you know the rules but are not overconfident. Here, ‘p’ is you win the game.

Therefore, option C is the correct answer.

Note:Sometimes we may encounter the word antecedent for the hypothesis and consequent for the conclusion, they are the same thing. Also, If the statement is correct, then the contrapositive is also logically correct. If the converse is correct, then the inverse is also logically correct.