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Answered 2014-05-01 08:21:01

No. It's not true for n=2, where 14n - 1 = 28 - 1 = 27, which is not

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The product of two integers is positive. when is this statement true?

This statement is true when the two integers are positive, or when the two integers are negative.

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

What is proof by induction?

Mathematical induction is just a way of proving a statement to be true for all positive integers: prove the statement to be true about 1; then assume it to be true for a generic integer x, and prove it to be true for x + 1; it therefore must be true for all positive integers.

Prove that if x and y are positive integers then x square plus y square is even but not divisible by 4?

The statement cannot be proven because it is FALSE. If one of x and y is odd and the other is even then x2 + y2 MUST be odd. Also if x and y are even then x2 + y2 MUST be divisible by 4. The statement is only true if x and y are odd integers. Whether or not they are positive makes little difference.

Some rational numbers are integers?

That's a true statement. Another true statement is: All integers are rational numbers.

What is the smallest number that can be divisible by all integers?

There does not exist a number that is divisible by all integers. The opposite is true. The number one can divided into all integers.

Is it true that no positive number is an integer?

No, integers can be positive or negative.

Is it true that there are no integers that are whole numbers?

No, integers are positive and negative whole numbers

Integers can be positive or negative true or false?

False - if the sentence is meant to be exhaustive. Integers can be positive or negative OR ZERO.

What is the sum is not divisible by 2 and not divisible by 4?

It is a statement which is true for some sums.

If a conditional statement is true then its contrapositive?

If a conditional statement is true then its contra-positive is also true.

Is the lowest common factor of any two positive integers always 1?

This statement is true because 1 is a factor of any 2 positive integers and so is always a common factor and since it is the smallest or lowest positive integer, it is always the lowest common factor.

Sum of three consecutive integers is divisible by three?

yes always this is true' example 1,2,3 sum is 6 and is divisible by 3

What is 360 divisible by 5?

It is a TRUE statement.

Is this biconditional statement true A number is divisible by 6 if and only if it is divisible by 3?

noIt is true that if a number is divisible by 6, it alsodivisible 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.http://wiki.answers.com/A_number_is_divisible_by_6_if_and_only_if_it_is_divisible_by_3&action=edit

What is true about any prime numbers?

They are positive integers with only two factors.

What is negation?

Negation is the opposite of something actual or positive. The negation of a true statement will be false. The negation of a false statement will be true.

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