Question

HURRY!!!!

If p -> q is true and q is true, then p is ____ true.
-always
-sometimes
-never
If p is true and q is true, then ~ p -> ~ q is ____ true.
-always
-sometimes
-never

Answer 1

Sometimes. p ⇒ q is true if both p and q are true, or whenever p is false.

Always. ¬ p ⇒ ¬q is true if ¬p and ¬q are both true (which means p and q are both false), or whenever ¬p is false (p is true).