No, it is not safe to mix Dawn dish soap (or any other dish soap) with bleach. Mixing bleach with certain types of dish soap or other cleaning products can produce toxic fumes and potentially harmful chemical reactions.
When bleach (sodium hypochlorite) comes into contact with certain ingredients commonly found in dish soaps, such as ammonia or acids, it can create chlorine gas. Chlorine gas is highly toxic and can cause respiratory problems, eye irritation, and other health issues. It is especially dangerous in enclosed spaces or if inhaled in high concentrations.
To ensure safety, it is best to use bleach and dish soap separately and follow the usage instructions on each product's label. If you need to clean surfaces with bleach and dish soap, it's recommended to clean them separately and rinse them thoroughly before switching to the other product.