Conditional Logic Quiz: 10 If-Then Puzzles to Solve
This conditional logic quiz tests how well you handle if-then rules, with questions on the contrapositive and the converse, the famous card puzzle known as the Wason selection task created by psychologist Peter Wason of University College London, a real-life version about drinking ages, only if and unless statements, if and only if rules, negations and chains of conditions. Ten questions.
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🎯 Daily Trivia Challenge • 🧠 10 Questions • ⏱️ 90 Seconds
Contrapositive
Which statement means the same as: If it is a dog, then it is a mammal?
Converse
What is the converse of the rule If P, then Q?
Cards
Four cards show A, K, 4 and 7. Rule: if a card has a vowel on one side, it has an even number on the other. Which cards must you turn over to test the rule?
Ages
Rule: if someone drinks beer, they must be over 18. Which two people must you check: a beer drinker, a cola drinker, a 25-year-old and a 16-year-old?
Homework
Rule: if you finish your homework, you can watch TV. You did not finish your homework. What does the rule say about watching TV?
Only if
You can enter the concert only if you have a ticket. Sam entered the concert. What follows?
Unless
The alarm rings unless the door is locked. The alarm did not ring. What follows?
If and only if
The light is on if and only if the switch is up. The light is off. What follows?
Negation
Which situation shows that the statement If it rains, I take an umbrella is false?
Chains
If it snows, school closes. If school closes, Mia stays home. It snows. What follows?
Your score
0/10
Scroll down to see the explanation for each question.
Explanations: answer key for all 10 questions
- Q1: Which statement means the same as: If it is a dog, then it is a mammal?
Answer: If it is not a mammal, then it is not a dog
This form is called the contrapositive, and it always has the same truth value as the original. The other two statements can be false even when the original is true.
- Q2: What is the converse of the rule If P, then Q?
Answer: If Q, then P
The converse swaps the two parts. A rule can be true while its converse is false: all dogs are mammals, but not all mammals are dogs.
- Q3: Four cards show A, K, 4 and 7. Rule: if a card has a vowel on one side, it has an even number on the other. Which cards must you turn over to test the rule?
Answer: A and 7
You must check A for an even number and 7 for a hidden vowel. The 4 cannot break the rule, whatever is on its back. Most people wrongly choose A and 4.
- Q4: Rule: if someone drinks beer, they must be over 18. Which two people must you check: a beer drinker, a cola drinker, a 25-year-old and a 16-year-old?
Answer: The beer drinker and the 16-year-old
Only the beer drinker and the 16-year-old could break the rule. This version is logically the same as the card puzzle, yet most people find it much easier.
- Q5: Rule: if you finish your homework, you can watch TV. You did not finish your homework. What does the rule say about watching TV?
Answer: The rule does not say
The rule only tells you what happens when homework is finished. Concluding that you cannot watch TV is a mistake called denying the antecedent.
- Q6: You can enter the concert only if you have a ticket. Sam entered the concert. What follows?
Answer: Sam has a ticket
Only if means having a ticket is a necessary condition. Anyone who entered must have one, though we do not know when Sam got it.
- Q7: The alarm rings unless the door is locked. The alarm did not ring. What follows?
Answer: The door is locked
Unless means if the door is not locked, the alarm rings. Since it did not ring, the door must be locked.
- Q8: The light is on if and only if the switch is up. The light is off. What follows?
Answer: The switch is down
If and only if works in both directions. The switch being up would mean the light is on, so with the light off the switch must be down.
- Q9: Which situation shows that the statement If it rains, I take an umbrella is false?
Answer: It rains and I do not take an umbrella
An if-then statement is broken only when the first part happens and the second part does not. All the other situations are consistent with the rule.
- Q10: If it snows, school closes. If school closes, Mia stays home. It snows. What follows?
Answer: Mia stays home
The rules form a chain: snow leads to school closing, which leads to Mia staying home. Chaining conditions like this is called a hypothetical syllogism.
Conditional Logic Quiz – Understanding If-Then Rules
Conditional statements, also called if-then statements, are everywhere: in rules, laws, contracts, computer programs and everyday promises. If you finish your homework, you can watch TV. If the payment is late, a fee is charged. Understanding exactly what such statements say, and what they do not say, is a powerful thinking skill.
Every conditional has two parts: the condition, or antecedent, and the result, or consequent. From a single rule, logicians build related statements. The contrapositive, if not Q then not P, always means the same as the original. The converse, if Q then P, and the inverse, if not P then not Q, may be false even when the rule is true.
In 1966, British psychologist Peter Wason created a famous experiment called the Wason selection task. People see four cards and must decide which to turn over to test a rule. Most choose the wrong cards. Yet when the same logic is presented as a rule about drinking ages, most people solve it easily, showing how context changes our reasoning.
Everyday language adds extra traps. Only if marks a necessary condition, unless means if not, and if and only if works in both directions. A rule is broken only when the condition happens and the result does not.
Computer programmers use conditional logic constantly, writing if statements that tell machines what to do in each situation. Lawyers and engineers also rely on precise conditions.
Practicing with if-then puzzles helps you read rules carefully, avoid common errors and argue more clearly.
What This Quiz Teaches
This quiz is perfect for students, programmers and logic fans.
- How if-then statements work
- The contrapositive and the converse
- The Wason selection task
- Only if, unless and if and only if
- When a conditional is broken
- Chains of conditions
Quick Facts About Conditional Logic
- Peter Wason first described his card task in 1966.
- In many studies, fewer than 10 percent of people solve the abstract card task correctly.
- Programming languages use if, else and then to control decisions.
- Denying the antecedent and affirming the consequent are classic fallacies.
- Contracts often use unless and provided that to set conditions.
- Logicians write if P then Q as an arrow from P to Q.
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