Asymptotic notations (Big O, Omega, Theta) have several properties: multiplication by a constant doesn't change the order; a function is Big O of itself; the transitive property holds; symmetry applies only to Theta; if f(n) is Big O of g(n), then g(n) is Omega of f(n); if f(n) is both Big O and Omega of g(n), then f(n) is Theta of g(n); and the Big O of a sum is the Big O of the maximum term; the Big O of a product is the Big O of the product of the individual Big Os. This segment delves into the transitive and symmetric properties of asymptotic notations. The presenter demonstrates the transitive property using a clear example involving Big O notation and then extends the concept to Omega and Theta notations. The explanation of the symmetric property, specifically its application to Theta notation, provides a comprehensive understanding of these fundamental properties. This segment explains the properties of asymptotic notations, specifically focusing on how multiplying a function by a constant does not change its Big O, Omega, or Theta classification. The presenter uses clear examples to illustrate this concept, making it easy to understand the impact of constant factors on asymptotic analysis.