Step 1: For a first-order reaction, the half-life is independent of the initial concentration of the reactant, and it remains constant regardless of how the concentration changes. Thus, Assertion (A) is false, but Reason (R) is true.
Step 2: Thus, Assertion (A) is false, and Reason (R) is true.
The decomposition of a compound A follows first-order kinetics. The concentration of A at time t = 0 is 1.0 mol L-1. After 60 minutes, it reduces to 0.25 mol L-1. What is the initial rate of the reaction at t = 0? (Take ln 2 = 0.693)
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\} $.