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Inference - Expert Level: invalid inference EXPERT

Strategic basic drills ★ for inference: 20 expert-level problems. Worksheet 29 of 30 - Focus: invalid inference. Develop expertise in logical inferences, implied meaning, deductive inference with step-by-step solutions. Ideal for expert-level learners targeting challenging problems and time-bound practice.

📝 Worksheet 29 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 29 of 30 (96% complete)

Question 1

Rule: If it's a holiday, schools are closed Observation: The school is open What can you logically infer?
This uses the contrapositive rule. The statement "If it's a holiday, schools are closed" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "The school is open" (the consequence is false), we can conclude "It's not a holiday" (the condition is false).
contrapositive, modus-tollens

Question 2

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 3

Analogical reasoning: "Birds build nests for their young. Bees build hives." What is the most reasonable inference by analogy?
This uses analogical reasoning: Birds build nests for their young. Bees build hives.

The analogy maps relationships from the source domain to the target domain, suggesting: Bees build hives for their young (the hive serves the same protective function as a nest)

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

Question 4

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 5

Given: All mammals breathe air. A dolphin is a mammal. What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "All mammals breathe air. A dolphin is a mammal." leads to "A dolphin breathes air" because the premise establishes a universal relationship and then confirms the condition.
direct, deductive, modus-ponens

Question 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

Rule: If it's a holiday, schools are closed Observation: The school is open What can you logically infer?
This uses the contrapositive rule. The statement "If it's a holiday, schools are closed" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "The school is open" (the consequence is false), we can conclude "It's not a holiday" (the condition is false).
contrapositive, modus-tollens

Question 14

Consider this argument: "She scored 100% on the test. She must be very intelligent." What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: High test scores indicate high intelligence (and the test was a valid measure of intelligence)

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 15

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 16

Given these logical premises: • If P, then Q • If Q, then R • If R, then S • Not S Which statement must be true?
This requires multi-step logical deduction:
• If P, then Q
• If Q, then R
• If R, then S
• Not S

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

Question 17

Consider these premises: • No criminals are honest • Some politicians are criminals • Robert is a politician Which conclusion logically follows?
By combining the premises logically:
• No criminals are honest
• Some politicians are criminals
• Robert is a politician

We can deduce: Robert may not be honest

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

Question 18

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 19

Analogical reasoning: "Birds build nests for their young. Bees build hives." What is the most reasonable inference by analogy?
This uses analogical reasoning: Birds build nests for their young. Bees build hives.

The analogy maps relationships from the source domain to the target domain, suggesting: Bees build hives for their young (the hive serves the same protective function as a nest)

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

Rule: If the store is open, lights are on Observation: The lights are off What can you logically infer?
This uses the contrapositive rule. The statement "If the store is open, lights are on" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "The lights are off" (the consequence is false), we can conclude "The store is closed" (the condition is false).
contrapositive, modus-tollens
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