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If…, then… – practice for Years 7–9

Sample questions on If…, then… with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Logic
Year
Years 7–9
Curriculum area
Statements and truth

Question types: What follows?

Rule: If…, then…

From “if P, then Q” and P, Q follows. From “if P, then Q” and “not Q”, “not P” follows.

Not the other way round: Q does not give you P, and “not P” does not give you “not Q”.

Example: If it rains, the ground is wet. The ground is dry, so it is not raining. The ground is wet? Then we can’t tell.

Watch out: “If it rains, the ground is wet” does not mean “if the ground is wet, it is raining”. The reverse rule doesn’t hold.

Sample questions

  1. Question 1 Easy

    The rule is: If it is Saturday, then Peter plays football. We know that it is Saturday. Decide whether each statement must follow (YES) or not (NO).

    1. Peter plays football.
    2. Peter does not play football.
    3. It is not Saturday.
    Show the solution
    Answer:
    1. Peter plays football. – yes
    2. Peter does not play football. – no
    3. It is not Saturday. – no

    How it works: 1. YES 2. NO 3. NO The rule also gives its contrapositive: if the second part is false, so is the first. The converse does not follow.

  2. Question 2 Normal

    The rule is: If it is raining, then Eva has an umbrella. We know that it is raining. Decide whether each statement must follow (YES) or not (NO).

    1. Eva does not have an umbrella.
    2. It is not raining.
    3. Eva has an umbrella.
    Show the solution
    Answer:
    1. Eva does not have an umbrella. – no
    2. It is not raining. – no
    3. Eva has an umbrella. – yes

    How it works: 1. NO 2. NO 3. YES The rule also gives its contrapositive: if the second part is false, so is the first. The converse does not follow.

  3. Question 3 Hard

    The rule is: If the number ends in 0, then the number is even. We know that the number is odd. Decide whether each statement must follow (YES) or not (NO).

    1. If the number is even, then the number ends in 0.
    2. If the number is odd, then the number does not end in 0.
    3. The number ends in 0.
    4. The number does not end in 0.
    5. The number is even.
    Show the solution
    Answer:
    1. If the number is even, then the number ends in 0. – yes
    2. If the number is odd, then the number does not end in 0. – yes
    3. The number ends in 0. – no
    4. The number does not end in 0. – yes
    5. The number is even. – no

    How it works: 1. YES 2. YES 3. NO 4. YES 5. NO The rule also gives its contrapositive: if the second part is false, so is the first. The converse does not follow.

Related topics

All Logic topics

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