Just for my own curiosity I compiled a list of 5 low carb foods that are in the top 10 (including both high and low carb) of each vitamin or mineral group. I did not always list the top ones just because I wanted to add variety to the list and not mention some of the same foods repeatedly.
Fat Solubles
Vitamin A - Liver, pumpkin, Spinach, Egg yolks, Mozzarella cheese
Vitamin D - Oysters, most fish, eggs, beef, cheddar cheese
Vitamin E - Sunflower seeds or oil, peanuts/butter/oil, Avocado, olive oil, mayonnaise
Vitamin K - Brussels sprouts, broccoli, cauliflower, swiss chard, beef
Water Soluble Vitamins
Vitamin C - Strawberries, tomatoes, red peppers, chili pepper, broccoli
Thiamin - Pork chops, ham, sunflower seeds, catfish, pea pods
Riboflavin - Beef liver, almonds, mackerel, clams, pork, chicken
Niacin - Beef liver, peanuts, chicken, tuna, mushrooms
Vitamin B12- clams, oysters, crab, trout, tuna
Folate - Chicken liver, broccoli, spinach, collared greens, romaine
Biotin - Peanuts, filberts, almonds, peanut butter, eggs
Pantothenic Acid - Sunflower seeds, salmon, poultry, avocados, mushrooms
Pyridoxine (B6) - Beef liver, salmon, chicken, turkey, avocado
Minerals
Calcium - Salmon, Swiss cheese, sardines, rhubarb, cottage cheese
Chromium - Broccoli, Turkey, Ham, Green Beans, onions
Copper - Beef liver, oysters, pumpkin seeds, unsweetened chocolate, tofu
Iodine - Salt, haddock, cottage cheese, shrimp, eggs, beef
Iron - Clams, liver, pumpkin seeds, beef, oysters
Magnesium - Almonds, peanuts, unsweetened chocolate, halibut, spinach
Manganese - Pecans, oysters, blackberries, spinach, pumpkin seeds
Molybdenum - Almonds, peanuts, eggs, tomatoes, cottage cheese
Phosphorus - Sardines, sunflower seeds, yogurt, salmon, chicken
Selenium - Brazil nuts, oysters, chicken liver, sardines, clams
Sodium - salt, pickles, canned broth, sauerkraut, soy sauce
Zinc - Oysters, pot roast, ground beef, turkey, chicken liver
Hope this list helps to ease your concerns.
If you are still curious, below I will post a sample standard (non crash diet) low fat day and a sample low carb (non induction) day and you can compare for yourself.
Low Fat
1351 Calories
27g fat
241g carbs
22g fiber
47g protein
Breakfast - a bowl of special k with skim milk
Midmorning snack - 1 serving of baked wheat thins with some fat free buttery spread
Lunch - Half a Subway low fat sandwich on wheat with baked potato chips and a banana
Midafternoon snack - Pretzels and diet drink
Dinner - Whole wheat Pasta with tomato sauce, a side salad with fat free dressing
Dessert - 1 scoop Fat Free frozen yogurt with a low fat vanilla wafer
After Dinner snack - Air popped popcorn
Low Carb Day
Calories - 1390
Fat - 79g
Carbs - 53
Fiber - 25 (less than 30g net carbs)
Protein - 127
Breakfast - omelette with mushrooms, spinach and cheese
Midmorning snack - 1oz mixed nuts
Lunch - Large Salad with hard boiled eggs, roast beef, turkey, blue cheese dressing and raspberries
Midafternoon snack - Celery with dip
Dinner - Salmon in a cream sauce with broccoli and mixed greens.
Dessert - Cottage cheese with cocoa and splenda
After Dinner snack - Sugar free jello with whipped cream
The low carb day ended up having slightly (under 40) more calories but the foods packed far more nutritional bang for your buck. I tried to be as fair as possible selecting whole wheat, low fat and fat free products which is exactly how I ate when I followed a low fat diet and would have thought that day was pretty healthy once upon a time. I think I will stick with my low carb.