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Inference - Intermediate-Advanced Level: inferential logic INTERMEDIATE-ADVANCED

Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level inference questions. Worksheet 20 of 30 hones your inferential logic abilities. Practice hidden meanings, implicit information, conclusion drawing under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.

📝 Worksheet 20 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 20 of 30 (66% complete)

Question 1

Statistical finding: A survey of 1000 randomly selected voters shows 55% support candidate X. Margin of error: ±3%. What can you infer about the population?
This uses statistical inference: from a representative sample, we can make probabilistic claims about the population. Candidate X likely has majority support (52-58% in the population) is the appropriate inference, accounting for sampling error and confidence levels.
sampling, generalization, confidence

Question 2

Consider these premises: • All doctors are educated • Some educated people are rich • Dr. Smith is a doctor Which conclusion logically follows?
By combining the premises logically:
• All doctors are educated
• Some educated people are rich
• Dr. Smith is a doctor

We can deduce: Dr. Smith is educated

This uses 3-step logical reasoning, applying transitive properties and categorical logic.
syllogism, chain-reasoning

Question 3

Statistical information: The probability of rain given dark clouds is 85%. The sky has dark clouds. What is the most reasonable inference?
This is probabilistic reasoning. The statistical evidence (The probability of rain given dark clouds is 85%. The sky has dark clouds.) doesn't guarantee certainty, but it provides strong support for: It will probably rain

Remember: Probability inferences are about likelihood, not certainty.
probabilistic, statistical, likelihood

Question 4

Quantifier logic: • All A are B • Some B are C • No C are D What can be inferred about the relationships?
This tests understanding of quantifiers (all, some, no, most). Some A may be C (but not necessarily)

Remember: 'Some' means 'at least one' (could be all). 'Most' means 'more than half'. No categorical statement about individuals follows from 'most' statements.
quantifiers, all-some-none, logic

Question 5

Observation: The patient has a fever and cough. Possible diagnoses: common cold, flu, COVID-19, or pneumonia. Which is the most reasonable inference about the cause?
This is abductive reasoning (inference to the best explanation). Given the observation 'The patient has a fever and cough. Possible diagnoses: common cold, flu, COVID-19, or pneumonia.', we consider possible causes and select the most plausible one. The flu is a likely diagnosis (given typical seasonal presentation) is the best explanation because it's the most common, simplest, or most likely cause.
abduction, best-explanation, diagnosis

Question 6

Observation: Crime rates fell after community policing was implemented What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Community policing likely reduced crime

However, be aware of alternative explanations (confounding variables, regression to the mean, etc.) that might also explain the observation.
causation, temporal, correlation

Question 7

Analogical reasoning: "A government's budget should be managed like a household budget." What is the most reasonable inference by analogy?
This uses analogical reasoning: A government's budget should be managed like a household budget.

The analogy maps relationships from the source domain to the target domain, suggesting: Governments should avoid deficit spending just as households should

Analogical inferences are suggestive but not logically certain; the strength depends on the relevance and similarity of the mapped features.
analogy, metaphor, mapping

Question 8

Consider this argument: "The team won the championship. They must have the best coach." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: Championship wins indicate best coaching (and the coach was the primary factor in the win)

This assumption is not explicitly stated but is necessary for the conclusion to follow from the premises. If this assumption is false, the argument becomes weak or invalid.
assumption, critical-thinking, argument-analysis

Question 9

Given these logical premises: • If A, then B • If B, then C • If C, then not D • A is true Which statement must be true?
This requires multi-step logical deduction:
• If A, then B
• If B, then C
• If C, then not D
• A is true

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: D is false
multi-step, quantifier, modal

Question 10

Logical condition: Being a mammal is necessary for being a dog. Fido is a dog. What can you infer?
This tests necessary vs. sufficient conditions.

- If A is SUFFICIENT for B: A → B (A guarantees B, but B can happen without A)
- If A is NECESSARY for B: B → A (B cannot happen without A)

Fido is a mammal
necessary-conditions, sufficient-conditions, logic

Question 11

Given: All prime numbers greater than 2 are odd. 7 is a prime number greater than 2. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "All prime numbers greater than 2 are odd. 7 is a prime number greater than 2." leads to "7 is odd" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens

Question 12

Rule: If it's a square, it has four sides Observation: This shape doesn't have four sides What can you logically infer?
This uses the contrapositive rule. The statement "If it's a square, it has four sides" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "This shape doesn't have four sides" (the consequence is false), we can conclude "This is not a square" (the condition is false).
contrapositive, modus-tollens

Question 13

Observation: Sales increased 40% after the advertising campaign What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: The advertising campaign likely caused increased sales

However, be aware of alternative explanations (confounding variables, regression to the mean, etc.) that might also explain the observation.
causation, temporal, correlation

Question 14

Consider these premises: • All mammals are warm-blooded • All whales are mammals • Moby is a whale Which conclusion logically follows?
By combining the premises logically:
• All mammals are warm-blooded
• All whales are mammals
• Moby is a whale

We can deduce: Moby is warm-blooded

This uses 3-step logical reasoning, applying transitive properties and categorical logic.
syllogism, chain-reasoning

Question 15

Analogical reasoning: "Keys unlock doors. Passwords unlock computers." What is the most reasonable inference by analogy?
This uses analogical reasoning: Keys unlock doors. Passwords unlock computers.

The analogy maps relationships from the source domain to the target domain, suggesting: Passwords function like digital keys (both provide authorized access to restricted spaces)

Analogical inferences are suggestive but not logically certain; the strength depends on the relevance and similarity of the mapped features.
analogy, metaphor, mapping

Question 16

Statistical finding: A drug trial with 500 patients found 80% improved. The control group had 30% improvement. What can you infer about the population?
This uses statistical inference: from a representative sample, we can make probabilistic claims about the population. The drug likely causes improvement (40% improvement over baseline is significant) is the appropriate inference, accounting for sampling error and confidence levels.
sampling, generalization, confidence

Question 17

Consider these premises: • No reptiles are warm-blooded • All snakes are reptiles • Python is a snake Which conclusion logically follows?
By combining the premises logically:
• No reptiles are warm-blooded
• All snakes are reptiles
• Python is a snake

We can deduce: Python is not warm-blooded

This uses 3-step logical reasoning, applying transitive properties and categorical logic.
syllogism, chain-reasoning

Question 18

Statistical information: 90% of lottery winners go bankrupt within 5 years. Maria won the lottery. What is the most reasonable inference?
This is probabilistic reasoning. The statistical evidence (90% of lottery winners go bankrupt within 5 years. Maria won the lottery.) doesn't guarantee certainty, but it provides strong support for: Maria will likely face financial difficulties

Remember: Probability inferences are about likelihood, not certainty.
probabilistic, statistical, likelihood

Question 19

Logical condition: Practice is necessary for mastery. Sarah has mastery. What can you infer?
This tests necessary vs. sufficient conditions.

- If A is SUFFICIENT for B: A → B (A guarantees B, but B can happen without A)
- If A is NECESSARY for B: B → A (B cannot happen without A)

Sarah practiced
necessary-conditions, sufficient-conditions, logic

Question 20

Logical condition: Fuel is necessary for a car to run. The car is running. What can you infer?
This tests necessary vs. sufficient conditions.

- If A is SUFFICIENT for B: A → B (A guarantees B, but B can happen without A)
- If A is NECESSARY for B: B → A (B cannot happen without A)

It has fuel
necessary-conditions, sufficient-conditions, logic
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