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10th grade If-then statements: converse, inverse, contrapositive and "if and only if" worksheet

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If-then statements: converse, inverse, contrapositive and "if and only if"

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Ari writes a rule on a sticky note: "If a number ends in 0, then it is even." Which part is the conclusion (the part right after "then")?

    • it is not even
    • it is even
    • a number ends in 0

  2. Bo writes a rule with a freshly sharpened pencil: "If a shape is a square, then it has four sides." Which part is the hypothesis (the part right after "if")?

    • a shape is not a square
    • a shape is a square
    • it has four sides

  3. Esme writes a rule in a puzzle book: "If an angle measures 30°, then it is acute." Which part is the conclusion (the part right after "then")?

    • an angle measures 30°
    • it is not acute
    • it is acute

  4. Jun writes a rule in a math notebook: "If a number is greater than 10, then it is greater than 5." Which part is the hypothesis (the part right after "if")?

    • a number is not greater than 10
    • it is greater than 5
    • a number is greater than 10

  5. Read this first

    Rule

    "If an angle measures 120°, then it is obtuse." New statement: "If an angle is not obtuse, then it does not measure 120°."

  6. Luz rewrites a rule in big crayon letters. The parts are P: "an angle measures 120°" and Q: "it is obtuse". What is the new statement called?

    • the contrapositive
    • the converse
    • the inverse
    • the same rule

  7. Rule

    "If a number is a multiple of 4, then it is even." New statement: "If a number is even, then it is a multiple of 4."

  8. Milo rewrites a rule for a number-sorting robot. The parts are P: "a number is a multiple of 4" and Q: "it is even". What is the new statement called?

    • the same rule
    • the inverse
    • the contrapositive
    • the converse

  9. Pia draws two circles on graph paper. Which if-then rule does the picture show?

    • If a number is a multiple of 10, then it is a multiple of 5.
    • If a number is a multiple of 5, then it is not a multiple of 10.
    • If a number is a multiple of 5, then it is a multiple of 10.

  10. Ren draws two circles with a pencil. Which if-then rule does the picture show?

    • If a whole number is odd, then it does not end in 5.
    • If a whole number is odd, then it ends in 5.
    • If a whole number ends in 5, then it is odd.

  11. Tala draws two circles on a card. Which if-then rule does the picture show?

    • If an angle is acute, then it measures 45°.
    • If an angle measures 45°, then it is acute.
    • If an angle is acute, then it does not measure 45°.

  12. Zee draws two circles in a notebook, one tucked inside the other. Which if-then rule does the picture show?

    • If a number is less than 8, then it is not less than 3.
    • If a number is less than 8, then it is less than 3.
    • If a number is less than 3, then it is less than 8.
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10th grade If-then statements: converse, inverse, contrapositive and "if and only if" worksheet – printable
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About this worksheet

If-then statements. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the hypothesis (after "if") and the conclusion (after "then") of a rule.
  • I can write the converse, inverse and contrapositive, and say which one always has the same truth value as the rule.
  • I can tell when a rule works both ways, so it can be written with "if and only if", and read it in symbols.

Standard: no CCSS standard (reasoning language that the proof standards G-CO.C.9–11 rely on)

Words to know

hypothesis: The part of an if-then rule right after "if".

conclusion: The part right after "then".

converse: The rule with its two parts swapped.

inverse: The rule with "not" added to both parts, same order.

contrapositive: Swap the parts and add "not" to both. Always as true as the rule.

counterexample: One case that fits the "if" part but breaks the "then" part.

biconditional: A rule that works both ways, written with "if and only if".

p → q, ~p: "If p, then q" and "not p".

Common mistakes

Your child mixed up the hypothesis (after "if") and the conclusion (after "then").

Your child mixed up the converse (swap the parts) with the contrapositive (swap and add "not"). Try: write one rule four ways and label each.

Your child mixed up the converse (swap the parts) with the inverse (add "not", same order). Try: underline the two parts of a rule, then swap them.

What to say

Ask: which part comes right after the word "if"?

Questions parents ask

What is the most common mistake with if-then statements: converse, inverse, contrapositive and "if and only if"?

Your child mixed up the hypothesis (after "if") and the conclusion (after "then").

How can I help my child with if-then statements: converse, inverse, contrapositive and "if and only if"?

Ask: which part comes right after the word "if"?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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