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

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

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

   • A rhombus with side 4 and angles of 60° and 120°
   • A rectangle that is 3 by 5
   • A square with side 4 and four right angles, drawn on the grid
   • An equilateral triangle with side 4
2. 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°
   • 30° and 60°
   • Two acute angles that add to 90°
   • 40° and 140°
3. 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 = -6
   • n = -5
   • n = 7
   • n = 4
4. 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?

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

   • At least one pencil in the box is not sharp
   • 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
6. 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. 7.

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

   • The triangle is acute and scalene
   • The triangle is not right
   • The triangle is not right and it is not isosceles
   • The triangle is not right or it is not isosceles
9. 8.

   In Pia's class of 40, 22 play soccer, 15 play chess and 6 play both. How many play neither?

   • 18
   • 31
   • 3
   • 9
10. 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?

    Use the picture in question 8.

    • 37
    • 25
    • 16
    • 31
11. 10.

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

    • 7
    • 10
    • 17
    • 27