In 16-bit 2's complement representation, the decimal number -28 is :

Consider three 4-variable functions f₁, f₂ and f₃, which are expressed in sum-of-minterms as

f₁ = Σ(0, 2, 5, 8, 14),

f₂ = Σ(2, 3, 6, 8, 14, 15),

f₃ = Σ(2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as :

Compute $$\mathop {\lim }\limits_{x \to 3} {{{x^4} - 81} \over {2{x^2} - 5x - 3}}$$

Let G be an arbitrary group. Consider the following relations on G :

R₁: ∀a,b ∈ G, aR₁b if and only if ∃g ∈ G such that a = g^-1bg

R₂: ∀a,b ∈ G, aR₂b if and only if a = b^-1

Which of the above is/are equivalence relation/relations?