Understanding the Generality of Logic Statements

[annoymage]

Homework Statement

sorry but I'm confused

is it okay if i say $$2 \leq 2$$ or $$1 \leq 2$$

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

 

[Mark44]

Homework Statement

sorry but I'm confused

is it okay if i say $$2 \leq 2$$ or $$1 \leq 2$$

Yes to both. For the first, $2 \leq 2$ 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.

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

Yes. Primes are considered to be positive integers that are greater than or equal to 2.

 

[annoymage]

aahhh~, thanks for clearing my mind