Let p, q, r be three logical statements. Consider the compound statements

$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)$$ and

$${S_2}:p \to (q \vee r)$$

Then, which of the following is NOT true?

Let R₁ and R₂ be relations on the set {1, 2, ......., 50} such that

R₁ = {(p, pⁿ) : p is a prime and n $$\ge$$ 0 is an integer} and

R₂ = {(p, pⁿ) : p is a prime and n = 0 or 1}.

Then, the number of elements in R₁ $$-$$ R₂ is _______________.

The number of real solutions of the equation $${e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0$$ is ___________.

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.