In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong.
Which of the following inference(s) is/are logically valid and can be inferred from the above passage?
i. His friends were always asking him to help them.
ii. He felt that when in need of help, his friends would let him down.
iii. He was sure that his friends would help him when in need.
iv. His friends did not help him last week.
A. (i) and (iii)
B. (iii) and (iv)
C. (iii) only
D. (iv) only
GATE 2016 · General Aptitude · Verbal Reasoning · medium
Answer: Statements (iii) and (iv) are the valid inferences. Answer: B.
Map the passage to logical propositions: P1: He always helped friends in need. P2: He was confident friends would reciprocate (help him when needed). P3: Events of last week proved him wrong.
Evaluate statement (iii): P2 directly states he was confident friends would help him. This is exactly what statement (iii) says. Valid inference.
Evaluate statement (iv): P2 says he expected friends to help. P3 says he was proved wrong. By modus tollens: if his confidence about help was proven wrong, then friends did NOT help him last week. Valid inference.
Eliminate statements (i) and (ii): Statement (i) - passage says he helped them, not that they always asked. Not inferable. Statement (ii) - he felt confident, not doubtful. This is the opposite of what is stated. Both are invalid.