Achieve proficiency in inferential logic by completing this worksheet
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Worksheet 19 of 30 (63% complete)
Question 1
Statistical finding: Of 50 randomly selected days, 40 were sunny. The region has 365 days per year.
What can you infer about the population?
This uses statistical inference: from a representative sample, we can make probabilistic claims about the population. Approximately 292 days per year are sunny in this region (80% of days) is the appropriate inference, accounting for sampling error and confidence levels.
Question 2
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
Question 3
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.
Question 4
Quantifier logic:
• Most students passed math
• Most students passed science
What can be inferred about the relationships?
This tests understanding of quantifiers (all, some, no, most). Some students passed both subjects
Remember: 'Some' means 'at least one' (could be all). 'Most' means 'more than half'. No categorical statement about individuals follows from 'most' statements.
Question 5
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.
Question 6
Consider these premises:
• All programmers write code
• Some code contains bugs
• Alice is a programmer
Which conclusion logically follows?
By combining the premises logically: • All programmers write code • Some code contains bugs • Alice is a programmer
We can deduce: Alice writes code
This uses 3-step logical reasoning, applying transitive properties and categorical logic.
Question 7
Logical condition: Being over 18 is necessary for voting. John can vote.
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)
John is over 18
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.
Question 9
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).
Question 10
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.
Question 11
Analogical reasoning:
"Plants need water to survive. Fish live in water."
What is the most reasonable inference by analogy?
This uses analogical reasoning: Plants need water to survive. Fish live in water.
The analogy maps relationships from the source domain to the target domain, suggesting: Fish have abundant access to what they need to survive (water provides oxygen and habitat like soil provides water and nutrients for plants)
Analogical inferences are suggestive but not logically certain; the strength depends on the relevance and similarity of the mapped features.
Question 12
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.
Question 13
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.
Question 14
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.
Question 15
Consider this argument:
"The new restaurant is always crowded. The food must be excellent."
What unstated assumption must be true for this reasoning to be valid?
The argument makes a hidden assumption: Crowded restaurants indicate excellent food (and not factors like location, price, or marketing)
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.
Question 16
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.
Question 17
Given: All roses are flowers. This is a rose.
What can you logically conclude?
This is a direct inference. The conclusion follows necessarily from the premise: "All roses are flowers. This is a rose." leads to "This is a flower" because the premise establishes a universal relationship and then confirms the condition.
Question 18
Observation: Water quality improved after the factory installed filters
What causal inference is most reasonable?
This inference uses temporal precedence (the cause occurred before the effect) and correlation to suggest causation: The filters likely improved water quality
However, be aware of alternative explanations (confounding variables, regression to the mean, etc.) that might also explain the observation.
Question 19
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
Question 20
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.