Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."
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Yoda cannot use a lightsaber and he will help Luke win the battle.
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If Yoda can help Luke win the battle, then he can use a lightsaber.
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Yoda can use a lightsaber if and only if he can help Luke win the battle.
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Yoda cannot use a lightsaber and will not help Luke win the battle.
In formal logic, a conditional statement 'If P then Q' is logically equivalent to its contrapositive 'If not Q then not P.' Here, P is 'Yoda cannot use a lightsaber' and Q is 'Yoda cannot help Luke.' The contrapositive is 'If Yoda CAN help Luke (not Q), then he CAN use a lightsaber (not P)' - which is option B. Options A and D assert conjunctions, not conditionals. Option C claims a biconditional (if and only if) which is stronger than the original.
The original statement is a conditional: 'not lightsaber → not help.' Its logical contrapositive — 'help → lightsaber' — is the only statement guaranteed to have the same truth value as the original. The other options either negate both parts (inverse), swap without negating (converse), or assert a biconditional, none of which are logically equivalent to the original conditional.