
Jesse E. answered 06/08/19
Experienced tutor for TEAS, chemistry, and biology
You are absolutely correct. There is even a table is freshman chemistry textbook showing strong acids producing weak conjugate bases and strong bases producing weak conjugate acids. This table in my textbook is called "Relative Strengths of Conjugate Acid-Base Pairs".
For example, as you are saying, HCl is strong acid. It has a weak conjugate base, -Cl. In contrast, Hydroxide is a strong base. it has a weak conjugate acid in water.