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Is The sum of any three consecutive integers is divisible by 3 Two integers are consecutive if and only if one is one more than the other is this true or false and what would be the counterexample?
Wiki User
∙ 9y ago
Both statements are true.
These should really be asked as two separate questions.
Yes, the sum of any three consecutive integers is divisible by 3. Call the first number "n", the other two will be "n + 1" and "n + 2". Adding everything together, you get 3n + 3, which is equal to 3(n + 1). Since "n" is a whole number, so is "n + 1", and 3 times as much is a multiple of 3.
Two integers are consecutive if one is one more than the other... Well, yes, that's basically the definition of "consecutive".
Wiki User
∙ 9y ago
Wiki User
∙ 9y agoThese should really be asked as two separate questions.
Yes, the sum of any three consecutive integers is divisible by 3. Call the first number "n", the other two will be "n + 1" and "n + 2". Adding everything together, you get 3n + 3, which is equal to 3(n + 1). Since "n" is a whole number, so is "n + 1", and 3 times as much is a multiple of 3.
Two integers are consecutive if one is one more than the other... Well, yes, that's basically the definition of "consecutive".
Wiki User
∙ 9y agoBoth statements are true.
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Any number that is divisible by 2 is also divisible by 6 Find a counterexample to show that the conjecture is false?
4 is divisible by 2 but not by 6
A number is divisible by 6 if and only if it is divisible by 3?
If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6. It becomes clearer if you split the question into its two parts. A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. A number is divisible by 6 only if it is divisible by 3? True.
True or False when you subtract a negative integer from another negative integer the result is always negative Explain.?
False. Counterexample: -1 - (-2) = -1 + 2 = 1.
True or false 6789 is it divisible by two?
False. If it doesn't end with a 2, 4, 6, 8, or 0, then it's not divisible by 2.
Is 0 an element of I the set of integers true or false?
It is true.
Is this statement true if the product of two integers is divisible by 6 one of the integers is also divisible by 6?
That is false. This type of statement is only true for prime numbers, not for compound numbers such as 6. Counterexample: 2 x 3 = 6
Any number that is divisible by 2 is also divisible by 6 Find a counterexample to show that the conjecture is false?
4 is divisible by 2 but not by 6
Any number that is divisible by 3 is also divisible by 9 .Find a counterexample to show that the conjecture is false?
You are an Idiot dude. there is no such value
Any number that is divisible by 4 is also divisible by 8 find a counterexample to show the conjecture is false?
4 divides 4 (once), but 4 is not divisible by 8. ■
A number is divisible by 6 if and only if it is divisible by 3?
If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6. It becomes clearer if you split the question into its two parts. A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. A number is divisible by 6 only if it is divisible by 3? True.
Specific case in which a statement is false?
A counterexample is a specific case in which a statement is false.
What is an example that shows a conjecture is false?
It's a counterexample.
A counterexample is sufficient to prove that a conjecture is false?
Yes.
A particular example or instance of a statement that makes a statement false?
Counterexample
Which counterexample shows that the conjectureevery four-sided figure is a parallelogram is false?
A trapezium.
Find a counterexample to the statement all us presidents have served only one term to show that this statement is false.?
find a counterexample to the statement all us presidents have served only one term to show statement is false
Is this biconditional statement true A number is divisible by 6 if and only if it is divisible by 3?
How can the following definition be written correctly as a biconditional statement? An odd integer is an integer that is not divisible by two. (A+ answer) An integer is odd if and only if it is not divisible by two
