Question

prove that log5isirrational

Answer 1

Let's assume the contrary - that log35=pqlog3⁡5=pq , p,q∈Np,q∈N. Then, we have 3p/q=53p/q=5, or 3p=5q3p=5q. This seems to suggest that 5 and 3 are not mutually prime; hence, reductio ad absurdum.

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Answer 2

Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty are
(A) Full: (REAR+1) mod n == FRONT, empty: REAR == FRONT
(B) Full: (REAR+1) mod n == FRONT, empty: (FRONT+1) mod n == REAR
(C) Full: REAR == FRONT, empty: (REAR+1) mod n == FRONT
(D) Full: (FRONT+1) mod n == REAR, empty: REAR == FRONT