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Inference - Beginner-Intermediate Level: certain inference BEGINNER-INTERMEDIATE

This deep dive ★ worksheet contains 20 beginner-intermediate-level inference problems. Worksheet 11 of 30 focuses on certain inference. Practice inductive reasoning, inferential logic, hidden meanings with our step-by-step solutions. Difficulty: building on fundamentals with moderate challenges. Recommended for developing learners.

📝 Worksheet 11 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 11 of 30 (36% complete)

Question 1

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 2

Rule: If you exercise regularly, you stay healthy Observation: John is not healthy What can you logically infer?
This uses the contrapositive rule. The statement "If you exercise regularly, you stay healthy" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "John is not healthy" (the consequence is false), we can conclude "John doesn't exercise regularly" (the condition is false).
contrapositive, modus-tollens

Question 3

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 4

Observation: Students' test scores improved by 25% after hiring new teachers What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: New teachers likely contributed to score improvement

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

Question 5

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 6

Observation: The grass is wet. It rained last night OR the sprinklers were on OR someone spilled water. Which is the most reasonable inference about the cause?
This is abductive reasoning (inference to the best explanation). Given the observation 'The grass is wet. It rained last night OR the sprinklers were on OR someone spilled water.', we consider possible causes and select the most plausible one. It probably rained last night (most common cause) is the best explanation because it's the most common, simplest, or most likely cause.
abduction, best-explanation, diagnosis

Question 7

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 8

Given: If you touch fire, you get burned. Tom touched fire. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "If you touch fire, you get burned. Tom touched fire." leads to "Tom got burned" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens

Question 9

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 10

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 11

Consider this argument: "Our competitor lowered prices and gained market share. We should lower ours too." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: Lowering prices will increase our market share (and our situation is identical to theirs)

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 12

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 13

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 14

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 15

Consider these premises: • If it's a weekend, we relax • If we relax, we watch movies • Today is Saturday Which conclusion logically follows?
By combining the premises logically:
• If it's a weekend, we relax
• If we relax, we watch movies
• Today is Saturday

We can deduce: We will watch movies

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

Question 16

Given these logical premises: • If it's Monday, then school is open • If school is open, then buses run • Buses are not running Which statement must be true?
This requires multi-step logical deduction:
• If it's Monday, then school is open
• If school is open, then buses run
• Buses are not running

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: It's not Monday
multi-step, quantifier, modal

Question 17

Given these logical premises: • All birds can fly • Penguins are birds but cannot fly • This statement is about typical birds • Tweety is a typical bird Which statement must be true?
This requires multi-step logical deduction:
• All birds can fly
• Penguins are birds but cannot fly
• This statement is about typical birds
• Tweety is a typical bird

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

Question 18

Given these logical premises: • Either John or Mary broke the vase • If John broke it, he would admit it • John didn't admit it Which statement must be true?
This requires multi-step logical deduction:
• Either John or Mary broke the vase
• If John broke it, he would admit it
• John didn't admit it

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Mary broke the vase
multi-step, quantifier, modal

Question 19

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 20

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
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