This discussion clarifies the validity of logic statements involving inequalities and implications. It confirms that both "2 ≤ 2" and "1 ≤ 2" are true, as the compound statement with OR holds true if at least one part is true. Additionally, it establishes that the statement "if p is prime then p > -20" is also true, as primes are defined as positive integers greater than or equal to 2, thus maintaining the generality of the implication.
PREREQUISITESStudents of mathematics, educators teaching logic and number theory, and anyone interested in understanding the foundations of logical reasoning and implications.
Yes to both. For the first, [itex]2 \leq 2[/itex] means that either 1) 2 < 2 (false) OR 2) 2 = 2 (true). For a compound statement with OR, the whole statement is true if either or both of the parts are true.annoymage said:Homework Statement
sorry but I'm confused
is it okay if i say [tex]2 \leq 2[/tex] or [tex]1 \leq 2[/tex]
Yes. Primes are considered to be positive integers that are greater than or equal to 2.annoymage said:and this example
i know this is true
"if p is prime then p>1"
but is this true?
"if p is prime then p>-20"
its true right? because the generality doesn't change