Question:

‘Only ignorant people believe in witchcraft’ is equivalent to:

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When you see “Only X are Y”, rewrite it as “All Y are X” to find the correct logical equivalent.
Updated On: Aug 14, 2025
  • Some ignorant persons are not those who believe in witchcraft.
  • All persons who believe in witchcraft are ignorant.
  • There is no link between ignorance and witchcraft.
  • No ignorant persons are those who do not believe in witchcraft.
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The Correct Option is B

Solution and Explanation

The statement “Only ignorant people believe in witchcraft” means that belief in witchcraft is restricted to the set of people who are ignorant.
In logic, when we say “Only X are Y”, it implies that all Y are included in the group X.
Here, “Only ignorant people are believers in witchcraft” means every believer in witchcraft must be an ignorant person.
So the correct equivalent is: “All persons who believe in witchcraft are ignorant.”
Option (a) “Some ignorant persons are not those who believe in witchcraft” may be true but does not capture the exact equivalence.
Option (c) “There is no link between ignorance and witchcraft” is the opposite of the original statement.
Option (d) “No ignorant persons are those who do not believe in witchcraft” changes the meaning completely — it implies all ignorant persons believe in witchcraft, which is not stated in the original.
Thus, the exact logical equivalent is option (b).
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