Which among the following are contradictory propositions :

(A) All judges are lawyers

(B) Some judges are lawyers

(C) No lawyers are judges

(D) Some judges are not lawyers

(E) Some lawyers are not judges

Choose the correct answer from the options given below:

The correct answer is - (A) and (D) Only

Key Points

• Contradictory Propositions
  • Two propositions are said to be contradictory if they cannot both be true at the same time and they cannot both be false at the same time.
  • Statement (A): "All judges are lawyers" implies that every single judge is a lawyer.
  • Statement (D): "Some judges are not lawyers" implies that there exists at least one judge who is not a lawyer.
  • Since statement (A) claims that every judge is a lawyer, it directly contradicts statement (D), which claims that there is at least one judge who is not a lawyer.

Additional Information

• Logical Relationships
  • Contradiction: Two statements are contradictory if one being true means the other must be false.
  • Contrary: Two statements are contrary if they cannot both be true, but they can both be false.
  • Subcontrary: Two statements are subcontrary if they cannot both be false, but they can both be true.
  • Subalternation: This refers to the logical relationship between a universal proposition and its corresponding particular proposition (e.g., "All S are P" and "Some S are P").
• Examples
  • Contradictory Example: "All cats are animals" vs. "Some cats are not animals" (cannot both be true or both be false).
  • Contrary Example: "All cats are black" vs. "No cats are black" (cannot both be true, but can both be false).
  • Subcontrary Example: "Some cats are black" vs. "Some cats are not black" (cannot both be false, but can both be true).
  • Subalternation Example: "All birds can fly" (universal) implies "Some birds can fly" (particular).