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Answered 2017-01-08 04:29:52

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

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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.


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


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


No, integers can be positive or negative.


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


No, integers are positive and negative whole numbers


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



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


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.


True. The product of 21 negative numbers will be negative.


False. Either the product or the quotient of two negative numbers is positive.False. Either the product or the quotient of two negative numbers is positive.False. Either the product or the quotient of two negative numbers is positive.False. Either the product or the quotient of two negative numbers is positive.



They are positive integers with only two factors.


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.


For the statement to be true it would need to have a positive truth value. A positive truth value cannot be derived from such ambiguous terms as we see here. Therefore, the statement is not true.



For positive integers, it is true that the largest factor of any number is itself


It is true, and it follows from the definition of multiplication and division.



Call the smaller of the two consecutive integers n. Then, from the problem statement: n(n+2) = 168, or n2 + 2n - 168 = 0, or (n + 14)(n - 12) = 0, which is true when n = -14 or +12. Therefore, the two integers sought are 12 and 14.


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.


Replace "not" with "1" and you have a true statement.





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