Inference - Intermediate Level: invalid inference INTERMEDIATE

Level up your inference skills with this comprehensive review. 20 intermediate-level problems await in Worksheet 14 of 30. Focus area: invalid inference. Learn implicit information, conclusion drawing, logical deduction through systematic practice. Designed for mid-level learners seeking moderate complexity with mixed patterns.

📝 Worksheet 14 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:

Develop winning strategies for implicit information
Learn smart approaches to conclusion drawing
Optimize your comprehensive review solving technique
Build strategic thinking in logical deduction
Master invalid inference through proven methods

Your progress through Inference

Worksheet 14 of 30 (46% complete)

Question 1

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 2

Given these logical premises: • All successful people work hard • Some hard workers are lucky • No lazy people are successful • John is successful Which statement must be true?

This requires multi-step logical deduction:
• All successful people work hard
• Some hard workers are lucky
• No lazy people are successful
• John is successful

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: John works hard

multi-step, quantifier, modal

Question 3

Statistical information: 7 out of 10 doctors recommend this medication. Your doctor prescribed it. What is the most reasonable inference?

This is probabilistic reasoning. The statistical evidence (7 out of 10 doctors recommend this medication. Your doctor prescribed it.) doesn't guarantee certainty, but it provides strong support for: This medication is probably effective

Remember: Probability inferences are about likelihood, not certainty.

probabilistic, statistical, likelihood

Question 4

Analogical reasoning: "Books store knowledge. Libraries store books." What is the most reasonable inference by analogy?

This uses analogical reasoning: Books store knowledge. Libraries store books.

The analogy maps relationships from the source domain to the target domain, suggesting: Libraries are repositories of knowledge (by storing books, libraries indirectly store the knowledge within them)

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

analogy, metaphor, mapping

Question 5

Observation: Several employees quit last month. Reasons could include low salary, poor management, better opportunities, or relocation. Which is the most reasonable inference about the cause?

This is abductive reasoning (inference to the best explanation). Given the observation 'Several employees quit last month. Reasons could include low salary, poor management, better opportunities, or relocation.', we consider possible causes and select the most plausible one. Better opportunities elsewhere is likely (most common reason for voluntary turnover) is the best explanation because it's the most common, simplest, or most likely cause.

abduction, best-explanation, diagnosis

Question 6

Rule: If you eat sugar, your energy increases Observation: Tom's energy didn't increase What can you logically infer?

This uses the contrapositive rule. The statement "If you eat sugar, your energy increases" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "Tom's energy didn't increase" (the consequence is false), we can conclude "Tom didn't eat sugar" (the condition is false).

contrapositive, modus-tollens

Question 7

Consider these premises: • If you practice daily, you improve • If you improve, you win matches • Sarah practices daily Which conclusion logically follows?

By combining the premises logically:
• If you practice daily, you improve
• If you improve, you win matches
• Sarah practices daily

We can deduce: Sarah will win matches

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

syllogism, chain-reasoning

Question 8

Quantifier logic: • Every musician can read music • Some singers cannot read music What can be inferred about the relationships?

This tests understanding of quantifiers (all, some, no, most). Some singers are not musicians

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 9

Statistical finding: A poll of 500 adults found 60% prefer product A over product B. What can you infer about the population?

This uses statistical inference: from a representative sample, we can make probabilistic claims about the population. Product A is likely preferred by most adults (within margin of error) is the appropriate inference, accounting for sampling error and confidence levels.

sampling, generalization, confidence

Question 10

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

Question 11

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 12

Consider this argument: "The ancient civilization built huge monuments, so they must have had advanced technology." What unstated assumption must be true for this reasoning to be valid?

The argument makes a hidden assumption: Advanced technology was necessary to build the monuments (and no other explanation like massive labor forces exists)

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 13

Quantifier logic: • Every musician can read music • Some singers cannot read music What can be inferred about the relationships?

quantifiers, all-some-none, logic

Question 14

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 15

Statistical information: Most car accidents occur within 5 miles of home. John had an accident 3 miles from home. What is the most reasonable inference?

This is probabilistic reasoning. The statistical evidence (Most car accidents occur within 5 miles of home. John had an accident 3 miles from home.) doesn't guarantee certainty, but it provides strong support for: This fits a common pattern

Remember: Probability inferences are about likelihood, not certainty.

probabilistic, statistical, likelihood

Question 16

Analogical reasoning: "Neurons transmit signals in the brain like wires transmit electricity." What is the most reasonable inference by analogy?

This uses analogical reasoning: Neurons transmit signals in the brain like wires transmit electricity.

The analogy maps relationships from the source domain to the target domain, suggesting: Neurons form a biological wiring system for information transmission

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

analogy, metaphor, mapping

Question 17

Rule: If it's a dog, it has fur Observation: Max doesn't have fur What can you logically infer?

This uses the contrapositive rule. The statement "If it's a dog, it has fur" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "Max doesn't have fur" (the consequence is false), we can conclude "Max is not a dog" (the condition is false).

contrapositive, modus-tollens

Question 18

Analogical reasoning: "Students study to pass exams. Athletes train to win competitions." What is the most reasonable inference by analogy?

This uses analogical reasoning: Students study to pass exams. Athletes train to win competitions.

The analogy maps relationships from the source domain to the target domain, suggesting: Training serves the same preparatory function for athletes as studying does for students

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

analogy, metaphor, mapping

Question 19

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 20

Given: If a number is divisible by 4, it's even. 16 is divisible by 4. What can you logically conclude?

This is a direct inference. The conclusion follows necessarily from the premise: "If a number is divisible by 4, it's even. 16 is divisible by 4." leads to "16 is even" because the premise establishes a universal relationship and then confirms the condition.

direct, deductive, modus-ponens

🎓 Level up your skills with Worksheet 14. Focus: invalid inference

Previous Worksheet Next Worksheet