QuestionFind a counterexample to show that the sum of two five-digit numbers can be a five-digit number.

Studdy Solution

STEP 1

Assumptions1. We are dealing with natural numbers. . Five-digit numbers are numbers that have exactly5 digits.
3. Six-digit numbers are numbers that have exactly6 digits.
4. The sum of two numbers is obtained by adding them together.

STEP 2

The statement we are trying to disprove is "The sum of two five-digit numbers is a six-digit number."

STEP 3

To disprove this statement, we need to find a counterexample. A counterexample is an example that disproves a statement or proposition. In this case, we need to find two five-digit numbers that, when added together, do not result in a six-digit number.

STEP 4

We can start by considering the smallest possible five-digit numbers. The smallest five-digit number is $10,000$ .

STEP 5

If we add two smallest five-digit numbers together, we get $10,000 +10,000 =20,000$

STEP 6

$20,000$ is a five-digit number, not a six-digit number. Therefore, this is a counterexample that disproves the statement.
The counterexample is $10,000 +10,000 =20,000$ .

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QuestionFind a counterexample to show that the sum of two five-digit numbers can be a five-digit number.

Studdy Solution

STEP 1

Assumptions1. We are dealing with natural numbers. . Five-digit numbers are numbers that have exactly5 digits.
3. Six-digit numbers are numbers that have exactly6 digits.
4. The sum of two numbers is obtained by adding them together.

STEP 2

The statement we are trying to disprove is "The sum of two five-digit numbers is a six-digit number."

STEP 3

To disprove this statement, we need to find a counterexample. A counterexample is an example that disproves a statement or proposition. In this case, we need to find two five-digit numbers that, when added together, do not result in a six-digit number.

STEP 4

We can start by considering the smallest possible five-digit numbers. The smallest five-digit number is $10,000$ .

STEP 5

If we add two smallest five-digit numbers together, we get $10,000 +10,000 =20,000$

STEP 6

$20,000$ is a five-digit number, not a six-digit number. Therefore, this is a counterexample that disproves the statement.
The counterexample is $10,000 +10,000 =20,000$ .

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QuestionFind a counterexample to show that the sum of two five-digit numbers can be a five-digit number.

Studdy Solution

STEP 1

Assumptions1. We are dealing with natural numbers. . Five-digit numbers are numbers that have exactly5 digits.3. Six-digit numbers are numbers that have exactly6 digits.4. The sum of two numbers is obtained by adding them together.

STEP 2

The statement we are trying to disprove is "The sum of two five-digit numbers is a six-digit number."

STEP 3

To disprove this statement, we need to find a counterexample. A counterexample is an example that disproves a statement or proposition. In this case, we need to find two five-digit numbers that, when added together, do not result in a six-digit number.

STEP 4

We can start by considering the smallest possible five-digit numbers. The smallest five-digit number is 10,00010,00010,000.

STEP 5

If we add two smallest five-digit numbers together, we get10,000+10,000=20,00010,000 +10,000 =20,00010,000+10,000=20,000

STEP 6

20,00020,00020,000 is a five-digit number, not a six-digit number. Therefore, this is a counterexample that disproves the statement.The counterexample is 10,000+10,000=20,00010,000 +10,000 =20,00010,000+10,000=20,000.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. We are dealing with natural numbers. . Five-digit numbers are numbers that have exactly5 digits.
3. Six-digit numbers are numbers that have exactly6 digits.
4. The sum of two numbers is obtained by adding them together.

We can start by considering the smallest possible five-digit numbers. The smallest five-digit number is $10,000$ .

If we add two smallest five-digit numbers together, we get $10,000 +10,000 =20,000$

$20,000$ is a five-digit number, not a six-digit number. Therefore, this is a counterexample that disproves the statement.
The counterexample is $10,000 +10,000 =20,000$ .