Consider the matrix R = \[\begin{bmatrix}1 & 2 & 4 & 8\\1 & 3 & 9 & 27\\1 & 4 & 16 & 64\\1 & 5 & 25 & 125\end{bmatrix}\]. The abso…

Let T be a full binary tree with 8 leaves. Suppose two leaves a and b are chosen uniformly and independently at random. The expect…

Suppose Y is distributed uniformly in the open interval (1, 6). The probability that the polynomial 3x^2 + 6xY + 3Y + 6 has only r…

Let U = {1, 2, ..., n} and A = {(x, X) | x ∈ X and X ⊆ U}. Consider the following two statements on |A|: I. |A| = n * 2^(n-1) II. …

Let X be a square matrix. Consider the following two statements on X: I. X is invertible II. Determinant of X is non-zero Which on…

Let G be an arbitrary group. Consider the following relations on G: R1: ∀a, b ∈ G, a R1 b if and only if ∃g ∈ G such that a = g^(-…