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.
(iii) and (iv)
Passage Analysis for Logical Inferences
The given passage presents a scenario where an individual consistently helped their friends in times of need. This individual was confident that their friends would "reciprocate," meaning they would return the favor and provide help when he needed it. However, the critical turning point is stated as: "However, the events of the last week proved him wrong." This sentence indicates that his confidence in his friends' reciprocity was unfounded, and something happened last week that contradicted his expectation.
Evaluating Each Inference Statement
To identify the logically valid inferences, we must determine which statements can be directly and unequivocally concluded from the information provided in the passage.
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(i) His friends were always asking him to help them.
The passage states, "He had always assisted them in times of need." While he consistently helped his friends, the text does not specify whether his friends "always asked" for his help. He might have proactively offered assistance, or they might have requested it only sometimes. The word "always" makes this inference too absolute and not directly supported by the passage. Therefore, this statement is not a logically valid inference.
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(ii) He felt that when in need of help, his friends would let him down.
On the contrary, the passage explicitly states, "He was confident that they would reciprocate." This means his initial belief was that his friends *would* help him, not let him down. The events of the last week "proved him wrong" about this confidence, but his *feeling* before those events was one of trust and certainty, not a premonition of being let down. Therefore, this statement is not a logically valid inference.
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(iii) He was sure that his friends would help him when in need.
The phrase "He was confident that they would reciprocate" directly supports this inference. "Confident" means being certain or sure. "Reciprocate" implies returning a favor, which, in this context, means his friends would help him when he was in need, just as he had helped them. This statement accurately reflects his strong expectation. Therefore, this statement is a logically valid inference.
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(iv) His friends did not help him last week.
The passage's crucial sentence, "However, the events of the last week proved him wrong," directly relates to his confidence in his friends' reciprocity. If his confidence in them helping him was "proved wrong" last week, it logically follows that when he needed help last week, his friends did not provide it. This inference is a direct consequence of his expectation being disproved. Therefore, this statement is a logically valid inference.
Conclusion on Valid Inferences
Based on a careful analysis of the passage, the logically valid inferences are (iii) and (iv). Inference (iii) accurately captures the protagonist's initial certainty regarding his friends' willingness to help him when he needed it. Inference (iv) correctly interprets the outcome of the events from the last week, which clearly contradicted his expectation of reciprocal help from his friends.
Thus, the statements (iii) and (iv) can be logically inferred from the provided passage.
Important Questions from Instructions
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statement:
I. All film stars are playback singers.
II. All film directors are film stars.
Conclusions:
I. All film directors are playback singers.
II. Some film stars are film directors.
All people in a certain are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.
P says “Both of us are knights”, Q says “None of us are knaves”.
Which one of the following can be logically inferred from the above?Fact: If it rains, then the field is wet.
Read the following statements:
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below is NOT logically possible, based on the given fact?A smart city integrates all modes of transport, uses clean energy and promotes the sustainable use of resources. It also uses technology to ensure the safety and security of the city, something which critics argue, will lead to a surveillance state.
Which of the following can be logically inferred from the above paragraph?
(i) All smart cities encourage the formation of surveillance states.
(ii) Surveillance is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a smart city.
(iv) There is a perception that smart cities promote surveillance.The binary operation □ is defined as a □ b = ab + (a + b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the number x such that a □ x = a, for any a, is_______.
