赤 and 青: color names and descriptive forms
Learn to name red and blue or use them to describe an object's color.
Naming the colors
赤, read あか, means red; 青, read あお, means blue. 好きな色は赤です。 says that the favorite color is red.
赤と青を選びました。 means choosing red and blue. It does not include the action of mixing them.
Modifying an object
赤いかばん and 青いかばん mean a red bag and a blue bag. The adjective forms add い to the color names 赤 and 青.
A form with の, such as 赤のかばん, is also possible. Seeing 赤い and 赤の does not license a na-adjective form such as 赤なかばん.
Choice and color change
青ではなく赤にしました。 means deciding on red rather than blue. The negative concerns the choice, not a failure to choose any color.
布を赤く染めました。 means dyeing cloth red. 赤く gives the resulting color.
Does 赤と青を選びました mean mixing the two colors?
Show the answer and why
No. It means selecting them. Mixing would need to be stated separately.