Based only on the truth of the statement ‘Some humans are intelligent’, which one of the following options can be logically inferred with certainty?

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), 𝑃(𝑥), of a variable x?

The James Webb telescope, recently launched in space, is giving humankind unprecedented access to the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and cosmologists believe that this odyssey in space may even shed light on the existence of dark matter. Dark matter is supposed to interact only via the gravitational interaction and not through the electromagnetic-, the weak- or the strong-interaction. This may justify the epithet “dark” in dark matter.

Based on the above paragraph, which one of the following statements is FALSE?

Let a = 30! , b = 50! , and c = 100! . Consider the following numbers:

log_a c, log_c a, log_b a, log_a b

Which one of the following inequalities is CORRECT?