Question

In a certain code language, '3a, 2b, 7c' means 'Truth is Eternal', '7c, 9a, 8b, 3a' means 'Enmity is not Eternal' and '9a, 4d, 2b, 8b' means 'Truth does not perish'. Which of the following means 'Enmity' in that language?

• A. 3a
• B. 7c
• C. 8b
• D. 9a

Hint:

Cancel out the codes shared by sentences that have 'is' and 'Eternal' or 'Truth' in common, to isolate 'Enmity'.

Answer 1

The Correct Option is C

Step 1: Match the two sentences that share "is" and "Eternal".
Sentence 1, "Truth is Eternal", is coded as 3a, 2b, 7c. Sentence 2, "Enmity is not Eternal", is coded as 7c, 9a, 8b, 3a. The words common to both sentences are "is" and "Eternal", and the codes common to both strings are 3a and 7c, so together \(\{3a, 7c\} = \{\text{is}, \text{Eternal}\}\).

Step 2: Match the sentences that share "Truth".
Sentence 3, "Truth does not perish", is coded as 9a, 4d, 2b, 8b. The only word common to sentence 1 and sentence 3 is "Truth", and the only code common to their strings is 2b, so \(2b = \text{Truth}\).

Step 3: Find what is left over in sentence 2.
Sentence 2 has four codes: 7c, 9a, 8b, 3a. We already know 3a and 7c stand for "is" and "Eternal", so the two codes left, 9a and 8b, must stand for the two words left in that sentence, "Enmity" and "not".

Step 4: Use sentence 3 to separate "not" from "Enmity".
"Not" is the one word sentence 2 and sentence 3 have in common, so its code must be common to both strings alongside 2b, which is already fixed as "Truth". Checking sentence 3, 9a is the code that fills this shared role, so \(9a = \text{not}\). That leaves 8b, the only code in sentence 2 not yet assigned to any other word, to stand for "Enmity".

Final Answer:
"Enmity" is coded as 8b. \[ \boxed{\text{8b (Option C)}} \]