Question

Based on the statements in (1) – (4), which option/s is/are correct?  
(1)   Thor has a female sibling                             
(2)   Thor has a sister
(3)   Thor has visited New Delhi
(4)   Thor has visited India

• (1) entails (2); (3) entails (4)
• (2) entails (1); (4) does not entail (3)
• (1) does not entail (2); (3) does not entail (4)
• (2) does not entail (1); (4) entails (3)

Hint:

In logical entailment, one statement entails another if the truth of the first guarantees the truth of the second. For example, "Thor has a female sibling" entails "Thor has a sister," and "Thor has visited New Delhi" entails "Thor has visited India."

Answer 1

The Correct Option is A, B

Step 1: Understanding the statements.
(1) "Thor has a female sibling" means that Thor has at least one sibling who is female.
(2) "Thor has a sister" implies that Thor has at least one female sibling. The two statements are effectively equivalent, so (1) entails (2).
(3) "Thor has visited New Delhi" means Thor has visited a specific city.
(4) "Thor has visited India" means Thor has visited a country that includes New Delhi as one of its cities. Since New Delhi is the capital of India, (3) entails (4).
Step 2: Analyzing the options.
(A) (1) entails (2); (3) entails (4):
Statement (1) does entail statement (2), as a "female sibling" is the same as a "sister."
Statement (3) does entail statement (4), as visiting New Delhi implies visiting India.
Therefore, option (A) is correct.
(B) (2) entails (1); (4) does not entail (3):
Statement (2) does entail statement (1), as "having a sister" means having a female sibling.
Statement (4) does not entail statement (3), as visiting India does not necessarily mean visiting New Delhi (there are many other cities in India).
Therefore, option (B) is also correct.
(C) (1) does not entail (2); (3) does not entail (4):
Statement (1) does entail statement (2), so this option is incorrect. (D) (2) does not entail (1); (4) entails (3):
Statement (2) does entail statement (1), so this option is incorrect.