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Inference - Advanced Level: certain inference ADVANCED

Master inference concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into certain inference while learning inferential logic, hidden meanings, implicit information. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 26 of 30 (86% complete)

Question 1

Given these logical premises: • All A are B • No B are C • All D are A • Some E are D Which statement must be true?
This requires multi-step logical deduction:
• All A are B
• No B are C
• All D are A
• Some E are D

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Some E are not C
multi-step, quantifier, modal

Question 2

Logical condition: Being over 18 is necessary for voting. John can vote. 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)

John is over 18
necessary-conditions, sufficient-conditions, logic

Question 3

Quantifier logic: • All dogs are mammals • No cats are dogs • Some pets are cats What can be inferred about the relationships?
This tests understanding of quantifiers (all, some, no, most). Some pets are not dogs

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 4

Observation: The car won't start. Possible causes: dead battery, empty gas tank, starter problem, or electrical issue. Which is the most reasonable inference about the cause?
This is abductive reasoning (inference to the best explanation). Given the observation 'The car won't start. Possible causes: dead battery, empty gas tank, starter problem, or electrical issue.', we consider possible causes and select the most plausible one. The battery is probably dead (most common cause) is the best explanation because it's the most common, simplest, or most likely cause.
abduction, best-explanation, diagnosis

Question 5

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 6

Statistical information: Only 10% of unprepared students get good grades. Sam is unprepared. What is the most reasonable inference?
This is probabilistic reasoning. The statistical evidence (Only 10% of unprepared students get good grades. Sam is unprepared.) doesn't guarantee certainty, but it provides strong support for: Sam will likely not get good grades

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

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

Observation: Traffic accidents decreased by 50% after installing speed cameras What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Speed cameras likely reduced traffic accidents

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

Question 9

Rule: If it's raining, there are clouds Observation: There are no clouds What can you logically infer?
This uses the contrapositive rule. The statement "If it's raining, there are clouds" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "There are no clouds" (the consequence is false), we can conclude "It's not raining" (the condition is false).
contrapositive, modus-tollens

Question 10

Consider this argument: "My phone battery died quickly. This new update must have caused it." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: The update is the cause of the battery drain (and no other apps or settings changed)

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 11

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 12

Given: If you study hard, you pass the exam. Mary studies hard. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "If you study hard, you pass the exam. Mary studies hard." leads to "Mary will pass the exam" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens

Question 13

Logical condition: Being a square is sufficient for being a rectangle. This shape is a square. 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 is a rectangle
necessary-conditions, sufficient-conditions, logic

Question 14

Observation: My computer is running slowly. It could have a virus, too many programs running, or low disk space. Which is the most reasonable inference about the cause?
This is abductive reasoning (inference to the best explanation). Given the observation 'My computer is running slowly. It could have a virus, too many programs running, or low disk space.', we consider possible causes and select the most plausible one. Too many programs are probably running (most common user issue) is the best explanation because it's the most common, simplest, or most likely cause.
abduction, best-explanation, diagnosis

Question 15

Statistical information: 75% of rainy days are cloudy. Today is rainy. What is the most reasonable inference?
This is probabilistic reasoning. The statistical evidence (75% of rainy days are cloudy. Today is rainy.) doesn't guarantee certainty, but it provides strong support for: Today is probably cloudy

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

Question 16

Observation: The light won't turn on. The bulb could be burned out, the switch broken, or there's no power. Which is the most reasonable inference about the cause?
This is abductive reasoning (inference to the best explanation). Given the observation 'The light won't turn on. The bulb could be burned out, the switch broken, or there's no power.', we consider possible causes and select the most plausible one. The bulb is likely burned out (most frequent cause) is the best explanation because it's the most common, simplest, or most likely cause.
abduction, best-explanation, diagnosis

Question 17

Observation: Hospital readmissions decreased after implementing follow-up calls What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Follow-up calls likely reduced readmissions

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

Question 18

Observation: Employee productivity increased after flexible work hours were introduced What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Flexible hours likely improved productivity

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

Question 19

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 20

Consider this argument: "Most successful entrepreneurs dropped out of college. If you want to be successful, you should drop out." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: College education prevents success (and the correlation represents causation)

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
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