List of top Data Science A.I Cyber Security and Computer Sci. Questions on Set Theory & Algebra

Let Σ be a finite non-empty alphabet and let 2Σ* be the power set of Σ*. Which one of the following is true?

Let A be a 2 × 2 matrix with elements $a_{11} = a_{12} = a_{21} = +1$ and $a_{22} = −1$. Then the eigenvalues of matrix A²are

The following system of equations: $$ x_1 + x_2 + x_3 = 1, \quad x_1 + 2x_2 + 3x_3 = 2, \quad x_1 + 4x_2 + \alpha x_3 = 4 $$ has a unique solution. Possible value(s) for $\alpha$ is/are:

If x ∈ [0, 1], and f(x) and g(x) are defined as: f(x) = sin(cos(πx/4)) and g(x) = cos(sin(πx/4)) then: