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Inference - Advanced Level: logical deduction ADVANCED

Level up your inference skills with this challenging mix. 20 advanced-level problems await in Worksheet 24 of 30. Focus area: logical deduction. Learn deductive inference, inductive reasoning, inferential logic through systematic practice. Designed for advanced learners seeking complex scenarios and multi-step problems.

📝 Worksheet 24 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Inference
Worksheet 24 of 30 (80% complete)

Question 1

Observation: Patient recovery times shortened after the new treatment was introduced What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: The new treatment likely accelerated recovery

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

Question 2

Rule: If you're over 18, you can vote Observation: Sarah cannot vote What can you logically infer?
This uses the contrapositive rule. The statement "If you're over 18, you can vote" is logically equivalent to its contrapositive: 'If NOT consequence, then NOT condition.' Since we observe "Sarah cannot vote" (the consequence is false), we can conclude "Sarah is under 18" (the condition is false).
contrapositive, modus-tollens

Question 3

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

Question 4

Logical condition: Practice is necessary for mastery. Sarah has mastery. 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)

Sarah practiced
necessary-conditions, sufficient-conditions, logic

Question 5

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 6

Statistical finding: Quality control tested 100 products and found 2 defects. The production run has 10,000 items. What can you infer about the population?
This uses statistical inference: from a representative sample, we can make probabilistic claims about the population. Approximately 200 items in the run are defective (based on 2% sample rate) is the appropriate inference, accounting for sampling error and confidence levels.
sampling, generalization, confidence

Question 7

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 8

Analogical reasoning: "Keys unlock doors. Passwords unlock computers." What is the most reasonable inference by analogy?
This uses analogical reasoning: Keys unlock doors. Passwords unlock computers.

The analogy maps relationships from the source domain to the target domain, suggesting: Passwords function like digital keys (both provide authorized access to restricted spaces)

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

Question 9

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 10

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 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

Statistical information: 80% of startups fail within 3 years. Alex just started a company. What is the most reasonable inference?
This is probabilistic reasoning. The statistical evidence (80% of startups fail within 3 years. Alex just started a company.) doesn't guarantee certainty, but it provides strong support for: Alex's company will probably fail within 3 years

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

Question 13

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 14

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 15

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 16

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 17

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 18

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 19

Observation: Customer complaints dropped by 70% after improving service training What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: Service training likely reduced complaints

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 these logical premises: • All X are Y • Some Y are Z • No Z are W • P is X Which statement must be true?
This requires multi-step logical deduction:
• All X are Y
• Some Y are Z
• No Z are W
• P is X

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