E is obviously false. Rest all are not completely specified, so fall under the "probably" category.
E is definitely false because of these statements
"Some good cooks are gourmet cooks ..."
"Some good cooks can be characterized as fast-food cooks..."
"Other good cooks are health food enthusiasts..."
Thus the set of good cooks include gourmet cooks, fast food cooks and health food enthusiasts.
"But even though not all good cooks are big eaters...".
This seals the fate for E.
Who says elephants can't dance?