Alexander turned his attention towards India, since he had conquered Persia. Which one of the statements below is logically valid and can be inferred from the above sentence?
Alexander would not have turned his attention towards India had he not conquered Persia.
Alexander's Expansion and Logical Inference
The question asks us to identify a logically valid statement that can be inferred from the sentence: "Alexander turned his attention towards India, since he had conquered Persia." This sentence establishes a cause-and-effect relationship, which is crucial for understanding the logical inference.
Understanding the Alexander Statement
Let's break down the given statement:
- Event 1 (Cause): Alexander had conquered Persia.
- Event 2 (Effect): Alexander turned his attention towards India.
The word "since" indicates that Event 1 is the reason or condition for Event 2. This can be rephrased as a conditional statement:
If Alexander had conquered Persia, then he turned his attention towards India.
In logical terms, if we represent "Alexander had conquered Persia" as P and "Alexander turned his attention towards India" as Q, the original statement implies: If P, then Q.
Evaluating Inferences from the Alexander Statement
We need to find an option that is a direct and necessary logical consequence of "If P, then Q".
Alexander's Attention: Analyzing Option 1
- Statement: "Alexander would not have turned his attention towards India had he not conquered Persia."
- Logical Form: This statement can be rephased as: "If Alexander had not conquered Persia (not P), then he would not have turned his attention towards India (not Q)."
- Validity: This is the contrapositive of the original conditional statement ("If P, then Q"). In logic, a conditional statement and its contrapositive are logically equivalent. If "If P, then Q" is true, then "If not Q, then not P" is also true. Similarly, "If not P, then not Q" (which is what Option 1 states) is also a valid inference if the original statement implies that conquering Persia was a *necessary* condition for turning attention to India. The word "since" strongly implies this necessity. If conquering Persia was the *reason* for turning attention to India, then without that reason, the attention would not have turned that way.
- Conclusion: This statement is a logically valid inference from the original sentence. The conquest of Persia is presented as a prerequisite for turning Alexander's attention towards India.
Alexander's Readiness: Analyzing Option 2
- Statement: "Alexander was not ready to rest on his laurels, and wanted to march to India."
- Analysis: This statement talks about Alexander's personal motivations or psychological state. The original sentence only states a cause-and-effect relationship between conquering Persia and turning attention towards India. It does not provide information about Alexander's general ambition or desire to "not rest on his laurels."
- Conclusion: This cannot be logically inferred from the given sentence alone. It introduces new information not present in the premise.
Alexander's Control: Analyzing Option 3
- Statement: "Alexander was completely in control of his army and could command it to move towards India."
- Analysis: This statement refers to Alexander's command authority and control over his army. While this might be historically accurate, the original sentence focuses on the *reason* Alexander turned his attention towards India (conquering Persia), not on his ability to execute the march. The sentence implies a decision or a shift in focus, not the logistical capability.
- Conclusion: This cannot be logically inferred. The original sentence does not provide any premise about Alexander's control over his army.
Alexander's Kingdom Extension: Analyzing Option 4
- Statement: "Since Alexander’s kingdom extended to Indian borders after the conquest of Persia, he was keen to move further."
- Analysis: This statement introduces two pieces of information not explicitly stated or necessarily implied by the original sentence:
- That Alexander's kingdom extended to Indian borders after the conquest of Persia.
- That he was "keen to move further" specifically because of this border extension.
- Conclusion: This cannot be logically inferred. It introduces additional assumptions and reasons not given in the initial premise.
Conclusion on Alexander's Inference
Based on the logical analysis of conditional statements, only the first option, "Alexander would not have turned his attention towards India had he not conquered Persia," is a valid logical inference. It is the contrapositive of the implied conditional statement "If Alexander conquered Persia, then he turned his attention towards India."
Important Questions from Verbal Deduction
Read the following paragraph and choose the correct statement.
Climate change has reduced human security and threatened human wellbeing. An ignored reality of human progress is that human security largely depends upon environmental security. But on the contrary, human progress seems contradictory to environmental security. To keep up both at the required level is a challenge to be addressed by one and all. One of the ways to curb the climate change may be suitable scientific innovations, while the other may be the Gandhian perspective on
Small scale progress with focus on sustainability.The American psychologist Howard Gardner expounds that human intelligence can be sub-categorised into multiple kinds, in such a way that individuals differ with respect to their relative competence in each kind. Based on this theory, modern educationists insist on prescribing multi-dimensional curriculum and evaluation parameters that enable the development and assessment of multiple intelligences.
Which of the following statements follows from the given text?
________ with someone else’s email account is now a very serious offence.
Most experts feel that in spite of possessing all the technical skills required to be a batsman of the highest order, he is unlikely to be so due to lack of requisite temperament. He was guilty of throwing away his wicket several times after working hard to lay a strong foundation. His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him.
Which of the statements (s) below is/are logically valid and can be inferred from the above passage?
i) He was already a successful batsman at the highest level
ii) He has to improve his temperament in order to become a great batsman
iii) He failed to make many of his good starts count
iv) Improving his technical skills will guarantee success.- Choose the statement where underlined word is used correctly.
