(a) What is the difference between native protein and denatured protein?
Native proteins are proteins that have their functional three-dimensional structure, which is necessary for their biological activity. They are in their natural, folded state with specific secondary, tertiary, and quaternary structures that are stabilized by various forces such as hydrogen bonding, hydrophobic interactions, and disulfide bonds. Denatured proteins, on the other hand, are proteins that have lost their natural structure due to the disruption of these stabilizing forces, often due to changes in temperature, pH, or chemical treatment. Denaturation results in the unfolding of the protein, causing it to lose its biological function.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.