Explain acid-base and their types according to $(A)$ Arrhenius and $(B)$ Bronsted-Lowry with examples.

(A-D) Arrhenius Acid-Base Theory: Strength is determined by the degree of ionization in aqueous solution.
- Strong Acids: Acids that undergo complete ionization in aqueous solution. Examples: Perchloric acid $(HClO_4)$,Hydrochloric acid $(HCl)$,Hydrobromic acid $(HBr)$,Hydroiodic acid $(HI)$,Nitric acid $(HNO_3)$,and Sulphuric acid $(H_2SO_4)$.
- Strong Bases: Bases that undergo complete ionization in aqueous solution. Examples: Lithium hydroxide $(LiOH)$,Sodium hydroxide $(NaOH)$,Potassium hydroxide $(KOH)$,Caesium hydroxide $(CsOH)$,and Barium hydroxide $(Ba(OH)_2)$.
- Weak Acid-Base: These undergo partial ionization in aqueous solution and exist primarily as unionized molecules. Examples: $Mg(OH)_2$ and $Ca(OH)_2$ are weak bases; $HCN, H_2S, H_3PO_4$ are weak acids.
$(B)$ Bronsted-Lowry Acid-Base Theory: $A$ strong acid is a good proton donor,and a strong base is a good proton acceptor.
- Strong Acid: Strong acids donate protons readily. Their conjugate bases are very weak. Examples: $(HClO_4, HCl, HBr, HI, HNO_3, H_2SO_4)$ are strong acids because they are excellent proton donors.
- Conjugate Bases: The conjugate bases of these strong acids,such as $(ClO_4^-, Cl^-, Br^-, I^-, NO_3^-, HSO_4^-)$,are much weaker bases than water.