Recall that .
So
But .
Now you show the others.
Can someone please explain how to verify/prove that:
((P => R1) ^ (P => R2)) <=> (P => (R1 ^ R2))
and
((R1 => P) ^ (R2 => P)) <=> ((R1 v R2) => P)
where "^" means "and", "=>" means "implies, and "<=>" means "equivalent to".
They're obviously equivalent from glance, but I just don't know how to mathematically verify them, ie, manipulate left and right sides so that they're identical.
Thanks.