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Quizzes > Personality & Relationships > Puzzles & Riddles

How Sharp Are Your Deductive Reasoning Skills? Take the Quiz!

Ready for tricky deductive reasoning questions? Challenge yourself now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art of logic puzzle pieces and question mark shapes on coral background for deductive reasoning quiz

Test your deductive reasoning with this free quiz of tricky deductive reasoning questions and deductive questions to sharpen your logic. In our deductive reasoning test with answers, you'll spot patterns, uncover hidden assumptions and get instant feedback to refine your skills. You'll learn to justify conclusions, test hypotheses and recognize valid inferences with every question. You'll even take a brief deductive vs inductive reasoning quiz to see how these methods contrast. Afterward, explore an inductive reasoning quiz or tackle a deductive argument for a deeper challenge. Let's begin and see your score climb!

Easy
Given that all cats are mammals, and all mammals are warm-blooded, which conclusion follows?
All mammals are cats.
Some warm-blooded animals are not cats.
All warm-blooded animals are cats.
All cats are warm-blooded.
By transitivity, if all cats are mammals and all mammals are warm-blooded, then all cats must be warm-blooded. The other options reverse or distort the relationships. https://en.wikipedia.org/wiki/Transitive_relation
Every artist is creative. Some musicians are artists. What must be true?
All musicians are creative.
Some artists are musicians.
All creative people are musicians.
Some musicians are creative.
Since some musicians fall into the group of artists, and all artists are creative, it follows that some musicians are creative. https://en.wikipedia.org/wiki/Category_syllogism
The butler is guilty or the maid is guilty. The butler is not guilty. Therefore, who is guilty?
The cook.
The maid.
The butler.
The guest.
Using the exclusive 'or' statement, if the butler is not guilty then the maid must be guilty. Other suspects are not part of the original disjunction. https://en.wikipedia.org/wiki/Exclusive_or
If it rains, the ground is wet. The ground is not wet. What can you conclude?
It rained.
Wet ground is always due to rain.
The ground caused the rain.
It did not rain.
This is an example of modus tollens: if P?Q and ¬Q, then ¬P. Here, P is 'it rains' and Q is 'ground is wet.' https://en.wikipedia.org/wiki/Modus_tollens
If it rains then I will carry an umbrella. It is not raining. What can you conclude?
I will carry an umbrella.
I carried an umbrella yesterday.
I may or may not carry an umbrella.
I will not carry an umbrella.
Denying the antecedent (not P) does not allow a valid conclusion about Q; the original implication only specifies what happens if it rains. https://en.wikipedia.org/wiki/Denying_the_antecedent
If A implies B, and B implies C, what can you deduce?
B implies A.
A implies C.
A and C are unrelated.
C implies A.
Implication is transitive: if A?B and B?C, then A?C must hold. https://en.wikipedia.org/wiki/Transitivity_(logic)
All birds can fly. Penguins are birds. Under these premises, can penguins fly?
Only some penguins can fly.
Cannot determine.
Yes.
No.
In deductive reasoning you accept given premises as true. Since all birds can fly and penguins are birds, then penguins can fly within this system. https://en.wikipedia.org/wiki/Deductive_reasoning
No cats are dogs. Some animals are cats. Which statement is necessarily false?
Some cats are dogs.
Some dogs are cats.
Some animals are dogs.
No animals are dogs.
Since cats and dogs do not overlap, the claim that some cats are dogs contradicts the first premise. https://en.wikipedia.org/wiki/Venn_diagram
Medium
Which of the following is the contrapositive of 'If p then q'?
If not q then not p.
If not p then q.
If not p then not q.
If q then p.
The contrapositive of P?Q is ¬Q?¬P, which is logically equivalent to the original. https://en.wikipedia.org/wiki/Contraposition
If coffee or tea is available, I will drink something. Coffee is not available. Which conclusion follows?
I will drink coffee.
Tea is not available.
I won't drink anything.
I will drink tea.
From P?Q and ¬P you can deduce Q by disjunctive syllogism. Here P is coffee, Q is tea. https://en.wikipedia.org/wiki/Disjunctive_syllogism
Which statement is equivalent to '¬(p ? q)'?
¬p ? ¬q
p ? q
p ? ¬q
¬p ? ¬q
By De Morgan's Law, ¬(P?Q) is equivalent to ¬P?¬Q. https://en.wikipedia.org/wiki/De_Morgan%27s_laws
The conditional 'If A then B' is false under which conditions?
A is false and B is true.
Both A and B are true.
Both A and B are false.
A is true and B is false.
A material implication P?Q is false only when P is true and Q is false. https://en.wikipedia.org/wiki/Material_conditional
Which is an example of a valid form of argument?
Modus ponens
Post hoc ergo propter hoc
Denying the antecedent
Affirming the consequent
Modus ponens (P?Q; P; therefore Q) is a valid deductive form. The others are informal or formal fallacies. https://en.wikipedia.org/wiki/Modus_ponens
If exactly one of P or Q is true, and P is false, what can you conclude?
Q is true.
Both P and Q are false.
Both P and Q are true.
Cannot determine.
An exclusive or means exactly one is true, so if P is false then Q must be true. https://en.wikipedia.org/wiki/Exclusive_or
What is the primary difference between a valid and a sound argument?
A sound argument is valid with true premises.
Every valid argument is unsound.
A valid argument has true premises.
Sound arguments do not need valid form.
Validity concerns correct logical form, while soundness requires both validity and true premises. https://en.wikipedia.org/wiki/Soundness_and_completeness
Hard
Three boxes are labeled 'Apples,' 'Oranges,' and 'Apples & Oranges,' but all labels are wrong. If you can pick one fruit from one box, which box guarantees you can relabel all correctly?
The box labeled 'Apples.'
The box labeled 'Apples & Oranges.'
The box labeled 'Oranges.'
Any box will work.
Since that box is mislabeled, it must contain only apples or only oranges. Tasting one fruit gives you its contents, letting you deduce all labels. https://en.wikipedia.org/wiki/Labeling_problem
You have three switches outside a closed room and three bulbs inside. You can flip switches and then enter once. How do you identify which switch controls which bulb?
You cannot determine with one visit.
Label switches arbitrarily and test.
Use heat from one bulb, on/off from another, leave one off.
Turn them all on then off in sequence.
Turn switch 1 on, leave it, turn switch 2 on briefly then off, leave switch 3 off. The hot bulb is switch 2, lit bulb is switch 1, unlit cold bulb is switch 3. https://en.wikipedia.org/wiki/Three_switches_and_three_bulbs_puzzle
A person on an island says, 'If I am a knight then 2+2=5.' Knights always tell the truth and knaves always lie. What is he?
Cannot determine.
An alternator.
A knave.
A knight.
The conditional is false only if he is a knight (true antecedent) but 2+2?5 (false consequent), which a knight cannot state. Thus he must be a lying knave. https://en.wikipedia.org/wiki/Knights_and_knaves
Four friends - Bob, Carla, Dave, and Emma - each have a different birthday month: January, February, March, and April. Anna's birthday is after Bob's but before Carla's. Who was born in March?
Emma.
Carla.
Dave.
Bob.
Sequence: Bob < Anna < Carla. The only three-month span is Jan - Feb - Mar, so Bob=Jan, Anna=Feb, Carla=Mar, leaving April. https://nrich.maths.org/2730
A car travels at 60 mph for one hour, then at 30 mph for one hour. What is its average speed?
45 mph
50 mph
60 mph
30 mph
Total distance is 60+30=90 miles over 2 hours, so average speed = 90/2 = 45 mph. https://en.wikipedia.org/wiki/Average_speed
Which of the following arguments commits the fallacy of affirming the consequent?
If it rains then the ground is wet. The ground is wet. Therefore it rained.
If A then B. If B then C. Therefore if A then C.
If p then q. Not q. Therefore not p.
All swans are white. This is a swan. Therefore it is white.
Affirming the consequent assumes Q?P from P?Q, which is invalid. Only the first example does this. https://en.wikipedia.org/wiki/Affirming_the_consequent
Given: If P then (Q and R); If not Q then S; S is false. What must be true?
P is true.
Q is true.
Either P is false or R is false.
R is false.
From ¬Q?S and ¬S, you get ¬¬Q so Q is true by contrapositive. No further deduction about P or R. https://en.wikipedia.org/wiki/Contraposition
Expert
Einstein's famous five-house puzzle concludes each house's owner and pet. Who owns the fish?
The Brit.
The Norwegian.
The German.
The Swede.
By systematically using the unique clues about colors, drinks, cigarettes, and pets, only the German ends up with the fish. https://en.wikipedia.org/wiki/Zebra_Puzzle
Which is the correct negation of the statement 'For all x, P(x)'?
Not for all x, P(x) and some P(x).
For all x, not P(x).
There exists x such that P(x).
There exists x such that not P(x).
The negation of ?x P(x) is ?x ¬P(x) by quantifier negation rules. https://en.wikipedia.org/wiki/Quantifier_(logic)#Negation
In a complex deductive system, how do you distinguish between necessary and sufficient conditions?
They are logically equivalent.
Necessary means both true, sufficient means both false.
A necessary condition must be satisfied for the conclusion, a sufficient one guarantees it.
A sufficient condition must be satisfied for the conclusion, a necessary one guarantees it.
A necessary condition is required but may not alone bring about the conclusion; a sufficient condition alone ensures the conclusion. https://en.wikipedia.org/wiki/Necessary_and_sufficient_conditions
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Study Outcomes

  1. Test Your Deductive Reasoning Skills -

    Engage with targeted scenarios to independently test your deductive reasoning and identify how you draw logical conclusions.

  2. Analyze Deductive Reasoning Questions -

    Break down each clue to pinpoint premises and assess the relationships needed to solve deductive questions.

  3. Apply Logical Inference Strategies -

    Use structured methods to infer accurate outcomes from given information and sharpen problem-solving speed.

  4. Differentiate Deductive vs Inductive Reasoning -

    Compare key traits of both reasoning styles to determine when to employ each approach effectively.

  5. Evaluate Answer Explanations -

    Review the deductive reasoning test with answers feedback to understand common pitfalls and reinforce correct logic.

  6. Measure Your Deductive Reasoning Performance -

    Track your quiz score to identify strengths and areas for growth as you refine your logical thinking.

Cheat Sheet

  1. Identify Premises and Conclusions -

    In deductive reasoning questions, accurately distinguishing premises (evidence) from the conclusion you must reach is crucial. For example, "All mammals are warm-blooded; whales are mammals; therefore whales are warm-blooded" clearly marks the first two statements as premises and the last as the conclusion (University of Cambridge Logic Group). Use the mnemonic "P before C" to remind yourself that premises always come before conclusions.

  2. Master Categorical Syllogisms -

    Categorical syllogisms form a backbone of many deductive reasoning tests with answers and rely on two premises leading to a necessary conclusion. Remember classic valid forms like Barbara (All M are P; All S are M; therefore All S are P) by using the "Barbara" mnemonic (Stanford University Philosophy Dept.). Practicing these structures regularly solidifies recognition of valid vs invalid forms.

  3. Ensure Validity and Soundness -

    Deductive arguments are only as strong as their logical structure and the truth of their premises - validity deals with form, while soundness requires true premises (Journal of Philosophy Logic). For instance, "All birds can swim; penguins are birds; therefore penguins can swim" may be valid in form but unsound in truth. When tackling deductive reasoning questions, first confirm validity then verify each premise.

  4. Differentiate Deductive and Inductive Reasoning -

    In a deductive vs inductive reasoning quiz, remember that deductive reasoning guarantees the conclusion if the premises are true, while inductive reasoning offers probable conclusions based on patterns (American Philosophical Association). A quick check: if the inference is 100% guaranteed by the premises, it's deductive. This clarity helps you select the right strategy under timed conditions.

  5. Sharpen Skills with Practice Tests -

    Consistent practice using free deductive reasoning tests with answers can significantly improve both accuracy and speed (GRE Official Guide). Set timed sessions focusing on different question types - syllogisms, propositional logic, and conditionals - to track progress and identify weak areas. Reviewing detailed answer explanations from reputable sources ensures you learn the reasoning behind each correct answer.

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