Questions: If-Then Statements

Question 1

In the statement 'If you eat your vegetables, then you can have dessert,' what is the condition and what is the result?

• A. Condition: you can have dessert. Result: you eat your vegetables.
• B. Condition: you eat your vegetables. Result: you can have dessert.
• C. Both parts are conditions
• D. Both parts are results

Answer: (B)

The condition (the 'if' part) is 'you eat your vegetables.' The result (the 'then' part) is 'you can have dessert.' The condition comes first and must be met for the result to follow. The order matters — reversing them would create a different statement with a different meaning.

Question 2

'If it rains, then the ground gets wet' means the same thing as 'If the ground is wet, then it rained.'

• T. True
• F. False

Answer: False

These are different statements. The original says rain causes wet ground. The reversed version says wet ground means it rained — but the ground could be wet for other reasons (sprinklers, a spilled bucket). Reversing an if-then statement creates a new statement that may or may not be true. This is one of the most important distinctions in logic: the original statement and its reverse (called the 'converse') are independent claims.

Question 3

Which of the following is an if-then statement?

• A. 'Dogs are animals' — a simple fact
• B. 'Is it cold outside?' — a question
• C. 'If a shape has three sides, then it is a triangle' — a conditional claim
• D. 'Please close the window' — a request

Answer: (C)

'If a shape has three sides, then it is a triangle' has the if-then structure: a condition (three sides) linked to a result (it is a triangle). The other options are a fact, a question, and a request — none have the conditional structure. Any sentence that links a condition to a consequence using 'if...then' is an if-then statement.

Question 4

Why is it wrong to reverse an if-then statement and assume the reverse is also true? Give an example.

Model answer: Reversing an if-then statement changes its meaning, and the reverse may be false even when the original is true. Example: 'If an animal is a dog, then it has four legs' is true. But the reverse, 'If an animal has four legs, then it is a dog,' is false — cats, horses, and many other animals also have four legs. The original says being a dog guarantees four legs. The reverse says four legs guarantee being a dog, which is a much stronger (and incorrect) claim.

This error — assuming the reverse of a true statement is also true — is called 'affirming the consequent' and is one of the most common logical fallacies. Teaching students to notice this at the if-then level builds resistance to this error in more complex reasoning.