洗剤 and 石鹸: cleaning products and intended uses
Name detergent and soap while separating intended use from actual use.
Detergent
洗剤 (せんざい) means detergent. 「食器用の洗剤を買いました」 means buying detergent for dishes.
「洗剤を少し入れました」 says a little detergent was added. 少し limits the amount but gives no exact measurement.
Soap
石鹸 (せっけん) means soap. 「石鹸で手を洗いました」 says the speaker washed their hands with soap.
「石鹸が小さくなりました」 says the soap became smaller. The sentence does not identify who used it.
Purpose and contrast
「手洗い用の石鹸」 identifies soap for handwashing. 用 describes purpose, not who is using it now.
「水だけでなく、洗剤も使いました」 says detergent was used as well as water. It does not negate the use of water.
Does 「洗剤を少し入れました」 establish an exact amount used?
Show the answer and why
No. It only says a small amount; an exact measurement requires further information.