Question

for each statement in 6 - 10, write a counterexample that disproves the statement.

1. if a student attends the junior/senior prom, the student is either a junior or a senior.
2. if someone owns a cell phone, they are able to access the internet from it.
3. when two numbers are added, the result will always be a larger number.
4. the product of two odd numbers will be even.
5. if a number is divisible by 2, it is also divisible by 4.

Explanation:

Step1: Analyze statement 6

A freshman could attend the junior/senior prom as a guest.

Step2: Analyze statement 7

There are old - fashioned cell phones without internet access.

Step3: Analyze statement 8

Adding a negative number to a number gives a smaller result. For example, $5+( - 3)=2$ and $2<5$.

Step4: Analyze statement 9

Let two odd numbers be $2n + 1$ and $2m+1$ where $n,m$ are integers. Then $(2n + 1)(2m + 1)=4nm+2n + 2m+1=2(2nm + n + m)+1$, which is odd. For example, $3\times5 = 15$ (odd).

Step5: Analyze statement 10

The number 2 is divisible by 2 but not by 4.

Answer:

1. A freshman attends as a guest.
2. An old - fashioned cell phone.
3. $5+( - 3)=2$ (where $2<5$).
4. $3\times5 = 15$ (odd).
5. The number 2.