$r:$All prime numbers are either even or odd, Is it a true statement?
I was studying Mathematical Logic then i came across above question.
Since here connecting word is "OR"
so if i separate two statement then it become
$p:$ All the prime number are even
$q:$ All the prime number are odd
Because both statement $p$ and $q$ are false so final statement $r$ must be false using truth value of statement for "OR" connective.
But my intuition says $r$ is true.
Am i thinking correct?
Please Help me in this.
Best Answer
You erroneously distributed the “all”. The correct interpretation is:
For every prime $p$: $p$ is even or $p$ is odd
Since every integer is either even or odd, we have:
($p$ is even or $p$ is odd) is true for all primes $p$
Therefore it is true — as your intuition suggested