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Inference - Intermediate Level: inference strength INTERMEDIATE

Boost your speed and accuracy with this adaptive style 📈 worksheet. Worksheet 15 of 30 presents 20 intermediate-level inference problems. Focus on inference strength while practicing logical inferences, implied meaning, deductive inference. Difficulty: moderate complexity with mixed patterns. Perfect for mid-level test takers.

📝 Worksheet 15 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 15 of 30 (50% complete)

Question 1

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 2

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 3

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 4

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 5

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 6

Consider these premises: • All squares are rectangles • No rectangles are circles • This shape is a square Which conclusion logically follows?
By combining the premises logically:
• All squares are rectangles
• No rectangles are circles
• This shape is a square

We can deduce: This shape is not a circle

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

Question 7

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 8

Given these logical premises: • Every cat is a mammal • No mammal can fly • Some pets are cats • Whiskers is a cat Which statement must be true?
This requires multi-step logical deduction:
• Every cat is a mammal
• No mammal can fly
• Some pets are cats
• Whiskers is a cat

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Whiskers cannot fly
multi-step, quantifier, modal

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

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 11

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

Question 12

Logical condition: Rain is sufficient for wet ground. The ground is wet. 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)

Cannot conclude it rained (could be sprinklers)
necessary-conditions, sufficient-conditions, logic

Question 13

Quantifier logic: • No reptiles have fur • All snakes are reptiles • Some pets are snakes What can be inferred about the relationships?
This tests understanding of quantifiers (all, some, no, most). Some pets do not have fur

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 14

Given: If it rains, the ground gets wet. It is raining. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "If it rains, the ground gets wet. It is raining." leads to "The ground is wet" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens

Question 15

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 16

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 17

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 18

Consider this argument: "Every time I wear this shirt, my team wins. This shirt brings good luck." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: The shirt causally influences game outcomes (and correlation implies 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

Question 19

Observation: Plant growth increased by 60% after adding fertilizer What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Fertilizer likely caused better plant growth

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

Question 20

Given: All birds have wings. A sparrow is a bird. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "All birds have wings. A sparrow is a bird." leads to "A sparrow has wings" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens
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