Let S be a finite set containing n elements. Then the total number of commutative binary operation on S is

• ${\mathrm{n}}^{\left[\frac{\mathrm{n}\left(\mathrm{n} + 1\right)}{2}\right]}$

• ${\mathrm{n}}^{\left[\frac{\mathrm{n}\left(\mathrm{n} - 1\right)}{2}\right]}$

• ${\mathrm{n}}^{\left({\mathrm{n}}^2\right)}$

• $2^{\left({\mathrm{n}}^2\right)}$

The output of the circuit is

• (x₂ + x₃) . [(x₁ · x₂) . x₃']

• (x₂ + x₃') . [(x₁ · x₂) . x₃']

• (x₂ + x₃) + [(x₁ · x₂) . x₃']

• (x₂ . x₃) . [(x₁ · x₂) . x₃']

The value of ${\log }_2\left(20\right){\log }_2\left(80\right) - {\log }_2\left(5\right){\log }_2\left(320\right)$ is equal to

• 5

• 6

• 7

• 8

Let B be a boolean algebra. If a, b $\in$ B, then (x - y)' is equal to

• a . b

• x . y'

• x' . y'

• x' + y'

The output of the circuit is

• x₃ . (x'₁ + x₂)

• (x'₃ + x₂) . x₁

• x'₃ . (x₁ + x₂)

• (x₁ + x₂) . x₃

The boolean expression corresponding to the combinational circuit is

• (x₁ + x₂ · x'₃)x₂

• (x₁ . (x₂ + x₃)) + x₂

• (x₁ . (x₂ + x'₃)) + x₂

• (x₁ + (x₂ + x'₃)) + x₃

107.

In a boolean algebra B with respect to '+' and '.', x' denotes the negation of x $\in$ B. Then

• x - x' = 1 and x · x' = 1

• x + x' = 1 and x . x' = 0

• x + x' = 0 and x . x' = 0

• x + x' = 0 and x . x' = 0

If a function f satisfies f {f(x)} = x + 1 for all real values of x and if f (0) = $\frac{1}{2}$, then f(1) is equal to

• $\frac{1}{2}$

• 1

• $\frac{3}{2}$

• 2

The domain of the function f(x) = log₂(log₃(log₄(x))) is

• $\left(- \infty , 4\right)$

• $\left(4, \infty \right)$

• (0, 4)

• $\left(1, \infty \right)$

If f : R $\to$ R and g : R $\to$ R are defined by f (x) = x - 3 and g(x) = x² + 1, then the values of x for which g{f(x)} = 10 are

• 0, - 6

• 2, - 2

• 1, - 1

• 0, 6