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10th grade Counterexamples, "not", "and", "or", and Venn diagrams worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Counterexamples, "not", "and", "or", and Venn diagrams

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Ari claims: every quadrilateral with four equal sides is a square. Which shape is a counterexample?

    • A rectangle that is 3 by 5
    • A square with side 4 and four right angles, drawn on the grid
    • A rhombus with side 4 and angles of 60° and 120°
    • An equilateral triangle with side 4

  2. A counterexample has two angles adding to 180° where one is not acute or one is not obtuse. Bo claims: if two angles add to 180°, one is acute and one is obtuse. Which pair is a counterexample?

    • 90° and 90°
    • 40° and 140°
    • Two acute angles that add to 90°
    • 30° and 60°

  3. a counterexample makes n² greater than 25 while n is not greater than 5. Esme claims: if n² > 25, then n > 5. Which value of n is a counterexample?

    • n = 4
    • n = 7
    • n = -6
    • n = -5

  4. Two diagonals bisect each other when each cuts the other at its midpoint. Jun claims: the diagonals of every quadrilateral bisect each other. Which shape is a counterexample?

    • Any quadrilateral whose diagonals are 5 and 7 long
    • A kite whose diagonals do not bisect each other
    • A triangle with three sides
    • A rectangle that is 4 by 6, with equal diagonals

  5. A negation is true exactly when the original statement is false. Kira says: all the pencils in the box are sharp. Which statement is the negation?

    • No pencil in the box is sharp, not even one of them
    • Some pencils in the box are sharp
    • The box has pencils in it
    • At least one pencil in the box is not sharp

  6. The rule is x > 5. The negation is true for exactly the numbers that do not satisfy the rule. A rule says x > 5. Luz writes the negation. Which statement is it?

    • x ≤ 5
    • x > -5
    • x = 5
    • x < 5

  7. The statement joins two facts with 'and'. Milo says: the triangle is right and isosceles. Which statement is its negation?

    • The triangle is not right
    • The triangle is acute and scalene
    • The triangle is not right or it is not isosceles
    • The triangle is not right and it is not isosceles

  8. p is true. q is false. p: a triangle has 3 sides (true). q: a square has 5 sides (false). Noah checks four statements. Which one is true?

    • p and q
    • p or q
    • not (p or q)
    • not p

  9. In Ren's class of 40, 22 play soccer, 15 play chess and 6 play both. How many play exactly one of the two?

    • 25
    • 31
    • 16
    • 37

  10. In Zee's class of 40, how many students play soccer but not chess?

    • 17
    • 27
    • 10
    • 7
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10th grade Counterexamples, "not", "and", "or", and Venn diagrams worksheet – printable
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About this worksheet

Counterexamples, not, and, or, and Venn diagrams. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find one case that breaks a claim, and say why a case that fits proves nothing.
  • I can write the negation of a statement, including the boundary of x > 5.
  • I can read a three-circle Venn diagram: count "and", "or", "not" and "exactly one", and find a missing part from a total.

Standard: no CCSS standard

Words to know

counterexample: One case that fits the "if" part of a claim but breaks the rest.

negation: The statement that is true exactly when the first one is false.

and (∧): True only when both parts are true; in a Venn diagram, the overlap.

or (∨): True when at least one part is true; both circles together.

not (~): Flips true and false; everything outside the circle.

→: "If …, then …"; false only when a true "if" leads to a false "then".

Venn diagram: Overlapping circles, one per group, with a count in each part.

Common mistakes

Gave an example that fits the claim. A counterexample must meet the 'if' part and break the 'then' part.

Gave a case that does not meet the 'if' part, so it says nothing about the claim. Check the 'if' first, then the 'then'.

Wrote the opposite instead of the negation. A negation is true exactly when the original is false.

Questions parents ask

What is the most common mistake with counterexamples, "not", "and", "or", and venn diagrams?

Gave an example that fits the claim. A counterexample must meet the 'if' part and break the 'then' part.

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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