Meaning: 'Named' means to give a title or designation to something, indicating that Mill identified this method specifically as the method of difference.

Wrong options:

• pointed: 'Pointed' suggests directing attention but does not convey the act of naming or designating, making it contextually inappropriate here.
• claimed: 'Claimed' implies asserting something as true, which does not fit the context of formally naming a method.
• demanded: 'Demanded' indicates a strong request or requirement, which does not align with the act of naming a method.

Correct answer: meant

Explanation: The word 'meant' is the past tense of 'mean,' which fits grammatically and contextually as it refers to what Mill intended or signified by the method of difference, maintaining the past narrative of the sentence.

Meaning: 'Meant' refers to the intention or significance behind something, indicating what Mill was conveying with his method.

Wrong options:

• capped: 'Capped' means to cover or limit, which does not relate to the context of explaining a concept or method.
• charged: 'Charged' implies assigning a responsibility or cost, which is not relevant to the context of explaining a scientific method.
• found: 'Found' suggests discovering something, which does not accurately reflect the act of explaining or defining a method.

Correct answer: respect

Explanation: The word 'respect' fits grammatically and contextually as it refers to the aspects or characteristics in which the two glasses of water are identical, aligning with the phrase 'identical in every respect.'

Meaning: 'Respect' in this context means 'aspect' or 'feature,' indicating the specific qualities being compared between the two glasses.

Wrong options:

• thought: 'Thought' refers to an idea or opinion, which does not fit the context of comparing physical characteristics.
• identity: 'Identity' refers to the state of being the same, but it does not work grammatically in this context as it does not fit the phrase structure.
• measure: 'Measure' implies quantifying something, which does not align with the qualitative comparison being made.

Correct answer: According

Explanation: The word 'According' fits grammatically as it introduces a clause that relates to Mill's method, indicating that the following statement is based on or in agreement with his method of difference.

Meaning: 'According' means 'in agreement with' or 'as stated by,' linking the subsequent explanation to Mill's methodology.

Wrong options:

• Compared: 'Compared' suggests a direct comparison, which does not grammatically fit as an introductory phrase for the following explanation.
• Contemporary: 'Contemporary' refers to something existing at the same time, which does not relate to the context of Mill's method.
• Sorted: 'Sorted' implies organizing or categorizing, which does not fit the grammatical structure needed to introduce Mill's method.

Correct answer: assume

Explanation: The word 'assume' fits grammatically and contextually as it indicates a conclusion drawn based on the method of difference, suggesting that it is reasonable to accept the change in color as a result of the ink's introduction.

Meaning: 'Assume' means to take something for granted or accept it as true without proof, which is appropriate in the context of scientific reasoning.

Wrong options:

• discuss: 'Discuss' implies talking about something, which does not fit the context of making a conclusion based on evidence.
• prefer: 'Prefer' indicates a choice or liking, which does not relate to the act of concluding or assuming based on evidence.
• acclaim: 'Acclaim' means to praise enthusiastically, which does not fit the context of making a logical assumption.

Correct answer: introduction

Explanation: The word 'introduction' fits grammatically as it refers to the act of bringing in a new factor, aligning with the context of the sentence regarding the change in color due to the ink.

Meaning: 'Introduction' means the act of bringing something into a situation, which in this case refers to the ink being added to the water.

Wrong options:

• magnitude: 'Magnitude' refers to size or extent, which does not relate to the act of adding a new factor in this context.
• preparation: 'Preparation' implies getting something ready, which does not fit the context of introducing a new element to the water.
• purification: 'Purification' refers to the process of making something clean, which does not relate to the introduction of a new factor affecting the water.