let p(n)=(5n-6)/3 is an integer be an open proposition over the domain of integer determine the truth value of
To determine the truth value of the open proposition p(n) = (5n - 6)/3 is an integer over the domain of integers, we need to consider if there exists any integer value of n for which p(n) gives an integer output.
In this case, we can rewrite the expression p(n) as follows: p(n) = (5n - 6)/3 = (5n/3) - 2
To check if p(n) is an integer for any integer value of n, we need to examine the term (5n/3). For (5n/3) to be an integer, n must be divisible by 3, since the numerator 5n contains a factor of 5, and the denominator 3 does not contain any factors of 5.
Now, let's consider the possible values of n. If n is any integer not divisible by 3, then (5n/3) will be a non-integer value. However, if n is a multiple of 3, then (5n/3) will be an integer.
Therefore, the truth value of the open proposition p(n) = (5n - 6)/3 is an integer over the domain of integers depends on the value of n. If n is a multiple of 3, then p(n) will be an integer. Otherwise, it will not be an integer.