Quiz 4: Logical Reasoning IQ Test: Deduce the Answer in 10 Questions

Read each scenario carefully and choose the most logically sound answer. Click Check My Logical IQ to see how sharp your reasoning skills really are!

1) All philosophers are thinkers. Some thinkers are writers. Therefore:

A) All writers are philosophers B) No philosophers are writers C) Some philosophers may be writers D) All thinkers are writers

2) If today is Thursday, then the day after tomorrow will be Saturday. Today is not Thursday. Therefore:

A) The day after tomorrow is Saturday B) We cannot determine what day it is C) The day after tomorrow is not Saturday D) Today is Friday

3) John is taller than Mike. Sarah is shorter than Mike. Which must be true?

A) Sarah is taller than John B) Mike is the tallest C) John is the shortest D) John is taller than Sarah

4) No reptiles are warm-blooded. All snakes are reptiles. Therefore:

A) No snakes are warm-blooded B) Some snakes are warm-blooded C) All warm-blooded animals are snakes D) Some reptiles are warm-blooded

5) If it rains, the game will be cancelled. The game was not cancelled. Therefore:

A) It rained B) It did not rain C) We cannot be sure if it rained D) The game was played indoors

6) All dogs are mammals. Some mammals are cats. Which conclusion follows?

A) All cats are dogs B) Some mammals are not dogs C) No dogs are cats D) All mammals are dogs or cats

7) Every time John eats peanuts, he gets a rash. John has a rash. Therefore:

A) John ate peanuts B) John is allergic to peanuts C) John should avoid peanuts D) John may have eaten peanuts

8) All squares are rectangles. All rectangles have four sides. Therefore:

A) All squares have four sides B) Some squares have three sides C) No rectangles are squares D) All four-sided shapes are squares

9) If the battery is dead, the car won't start. The car started. Therefore:

A) The battery is not dead B) The battery is dead C) The battery has charge D) The car has a new battery

10) Some doctors are researchers. All researchers are scientists. Therefore:

A) All scientists are doctors B) Some doctors are scientists C) No doctors are scientists D) All doctors are scientists

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Logical reasoning is essential for programming, law, research, and any field requiring clear, structured thinking!

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Answers and Clarifications

Understand the logical reasoning behind each solution. Click on any question below to view its detailed explanation.

Question 1: Syllogistic Reasoning

Correct Answer: C) Some philosophers may be writers

This is a categorical syllogism:

• Premise 1: All philosophers are thinkers
• Premise 2: Some thinkers are writers
• Conclusion: Some philosophers may be writers

We cannot conclude "all philosophers are writers" because only some thinkers are writers. However, since all philosophers are thinkers, and some thinkers are writers, it's possible that some philosophers are among those thinkers who are writers.

Question 2: Conditional Logic

Correct Answer: B) We cannot determine what day it is

This tests understanding of conditional statements:

• The statement "If today is Thursday, then the day after tomorrow is Saturday" is true
• But we're told "Today is not Thursday"
• When the condition (today is Thursday) is false, we cannot determine the truth of the consequence

If today were Monday, Tuesday, Wednesday, Friday, Saturday, or Sunday, the day after tomorrow would not be Saturday. We simply don't have enough information.

Question 3: Transitive Reasoning

Correct Answer: D) John is taller than Sarah

This uses transitive reasoning:

• John > Mike (John is taller than Mike)
• Mike > Sarah (Mike is taller than Sarah, since Sarah is shorter than Mike)
• Therefore: John > Mike > Sarah, so John > Sarah

We cannot determine if Mike is tallest (there could be someone taller than John) or if John is shortest (there could be someone shorter than Sarah). But the transitive relationship guarantees John is taller than Sarah.

Question 4: Categorical Logic

Correct Answer: A) No snakes are warm-blooded

This uses categorical syllogism:

• Premise 1: No reptiles are warm-blooded
• Premise 2: All snakes are reptiles
• Conclusion: No snakes are warm-blooded

If all snakes belong to the category of reptiles, and no reptiles have the property of being warm-blooded, then no snakes can be warm-blooded.

Question 5: Denying the Consequent

Correct Answer: C) We cannot be sure if it rained

This tests understanding of conditional logic:

• Statement: If P (rains) then Q (game cancelled)
• We know: Not Q (game not cancelled)
• We cannot conclude: Not P (did not rain)

The game could have been cancelled for other reasons besides rain. Just because the game wasn't cancelled doesn't mean it didn't rain - maybe they played in the rain, or the game was indoors.

Question 6: Set Theory Logic

Correct Answer: B) Some mammals are not dogs

This uses set theory reasoning:

• Dogs ⊂ Mammals (all dogs are mammals)
• Cats ⊂ Mammals (some mammals are cats)
• Since cats exist as mammals, and dogs don't include all mammals, some mammals must not be dogs

We cannot conclude anything about the relationship between dogs and cats specifically, only that the mammal category contains more than just dogs.

Question 7: Correlation vs Causation

Correct Answer: D) John may have eaten peanuts

This tests understanding of logical necessity:

• We know: Eating peanuts → Rash (whenever John eats peanuts, he gets a rash)
• We observe: Rash
• We cannot conclude: Ate peanuts (this would be affirming the consequent fallacy)

John could have gotten the rash from other causes (other foods, allergies, skin conditions). We can only say peanuts are one possible cause, not the certain cause.

Question 8: Logical Deduction

Correct Answer: A) All squares have four sides

This uses simple deductive reasoning:

• Premise 1: All squares are rectangles
• Premise 2: All rectangles have four sides
• Conclusion: All squares have four sides

If every square is a rectangle, and every rectangle has four sides, then every square must have four sides. This is a valid deductive argument.

Question 9: Modus Tollens

Correct Answer: C) The battery has charge

This uses the logical rule of Modus Tollens:

• If P (battery dead) then Q (car won't start)
• Not Q (car started)
• Therefore: Not P (battery not dead)

This is valid reasoning. If the battery were dead, the car wouldn't start. Since the car started, the battery cannot be dead, so it must have charge.

Question 10: Chain Reasoning

Correct Answer: B) Some doctors are scientists

This uses chain reasoning:

• Some doctors are researchers
• All researchers are scientists
• Therefore: The doctors who are researchers must also be scientists
• Thus: Some doctors are scientists

We cannot conclude "all doctors are scientists" because only some doctors are researchers. But those doctors who are researchers must be scientists since all researchers are scientists.

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Logical reasoning involves identifying valid arguments, avoiding fallacies, and drawing sound conclusions from given premises.

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