Question

for each statement in 6 - 10, write a counterexample that disproves the statement. 6. mary enters her home and her clothes are wet. therefore, it is raining outside. 7. if a number is multiplied to another number, it will result in a larger number. 8. if a figure has four sides and all sides have the same length, it is a square. 9. if a number is prime, then it is an odd number. 10. yvette lives in jacksonville. therefore, she lives in florida.

Explanation:

• For statement 6, there are other reasons for clothes to get wet. For statement 7, multiplying by a fraction or negative number can result in a smaller number. For statement 8, a rhombus has four equal - length sides but is not always a square. For statement 9, 2 is a prime number but is even. For statement 10, there are other places named Jacksonville in the US.

Answer:

• 6. Mary was splashed by a water hose inside before entering.
• 7. \(2\times0.5 = 1\), and \(1<2\).
• 8. A rhombus has four equal - length sides but is not a square (as its angles are not all right angles).
• 9. The number 2 is prime but it is an even number.
• 10. There is a Jacksonville in North Carolina, so she may not be in Florida.