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

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   "If a number is even, then it is a multiple of 4." Kira knows the rule on the card is false. Which statement must also be false?

   • If a number is not even, then it is not a multiple of 4.
   • If a number is a multiple of 4, then it is not even.
   • If a number is a multiple of 4, then it is even.
   • If a number is not a multiple of 4, then it is not even.
2. 2.

   "If a shape has four sides, then it is a square." Luz knows the rule on the card is false. Which statement must also be false?

   • If a shape is a square, then it has four sides.
   • If a shape is a square, then it does not have four sides.
   • If a shape is not a square, then it does not have four sides.
   • If a shape does not have four sides, then it is not a square.
3. 3.

   "If an angle measures 89°, then it is acute." Milo knows the rule on the card is true. Which statement must also be true?

   • If an angle is acute, then it measures 89°.
   • If an angle is acute, then it does not measure 89°.
   • If an angle does not measure 89°, then it is not acute.
   • If an angle is not acute, then it does not measure 89°.
4. 4.

   "If a number is greater than 100, then it is greater than 60." Noah knows the rule on the card is true. Which statement must also be true?

   • If a number is greater than 60, then it is greater than 100.
   • If a number is greater than 60, then it is not greater than 100.
   • If a number is not greater than 60, then it is not greater than 100.
   • If a number is not greater than 100, then it is not greater than 60.
5. 5.

   Pia wants a rule for the math club poster that works both ways. Which rule can be written with "if and only if"?

   • If a whole number ends in 6, then it is even.
   • If a polygon has five sides, then it is a pentagon.
   • If an angle is acute, then it measures 40°.
   • If a number is a multiple of 3, then it is odd.
6. 6.

   Ren wants a rule for the math club poster that works both ways. Which rule can be written with "if and only if"?

   • If a number is a multiple of 50, then it is a multiple of 10.
   • If two angles add to 90°, then they are complementary.
   • If a number is greater than 5, then it is greater than 9.
   • If a number is a multiple of 5, then it is odd.
7. 7.

   Zee wants a rule for the math club poster that works both ways. Which rule can be written with "if and only if"?

   • If a whole number is odd, then it ends in 5.
   • If an angle is acute, then it measures 10°.
   • If x − 3 = 5, then x = 8.
   • If a number is less than 1, then it is less than 10.

8. Read this first

   Use this

   p: "a number ends in 8". q: "a number is even". The rule p → q is "If a number ends in 8, then it is even."

9. 8.

   Ari codes a rule for a number-sorting robot. Which sentence does ~q → ~p say?

   • If a number is not even, then it does not end in 8.
   • If a number is even, then it ends in 8.
   • If a number does not end in 8, then it is not even.
   • If a number is even, then it does not end in 8.

10. Use this

    p: "a number is a multiple of 14". q: "a number is a multiple of 7". The rule p → q is "If a number is a multiple of 14, then it is a multiple of 7."

11. 9.

    Bo writes the converse of p → q on a sheet of paper. Which symbols show the converse?

    • q → p
    • ~p → ~q
    • ~q → ~p
    • p → ~q

12. Use this

    p: "an angle measures 35°". q: "an angle is acute". The rule p → q is "If an angle measures 35°, then it is acute."

13. 10.

    Esme writes a rule in pencil, in symbols. Which sentence does ~q → ~p say?

    • If an angle is acute, then it does not measure 35°.
    • If an angle does not measure 35°, then it is not acute.
    • If an angle is acute, then it measures 35°.
    • If an angle is not acute, then it does not measure 35°.