No! You guys are both wrong!
Mother Mothra was killed by Godzilla. Seriously.
She came to defend her two eggs from Godzilla approaching them for a tasty omelette. She put up a good fight, but Godzilla roasted her with his radiation fire blast and she went down and died. But she was successful in defending her offspring, as Godzilla went off to do some other human damage.
The two moths hatch as tough little silk spewing larva tanks. So there're more moths.
You guys got to checkout Godzilla Vs the Thing (1964), it's beautifully colored, funny, has the best song in monster film history, a wild sci-fi fantasy film, and it's the best Godzilla film all time.
I'm going to give yous another True or False:
In the original 1933 King Kong classic, you never see King Kong crashing through the giant logged fence built by the natives to keep Kong out.