Step 1: Recall soap definition.
Soaps are sodium or potassium salts of long-chain fatty acids.
Step 2: Check options.
- (A) C$_{17}$H$_{35}$COONa: Sodium stearate, a typical soap.
- (B) (C$_{17}$H$_{35}$COO)$_2$Ca: Insoluble salt (scum in hard water), not a soap.
- (C) C$_{17}$H$_{35}$COOH: Stearic acid, not soap.
- (D) C$_{15}$H$_{31}$COOH: Palmitic acid, also not soap.
Step 3: Conclusion.
Thus, the correct soap is C$_{17$H$_{35}$COONa}.