Explanation

(c)
Given probability of speaking truth are
$P(A) = \frac{4}{5}\ and\ P(B) = \frac{3}{4}$
And their corresponds probabilities of not speaking truth are
$P(\overline{A}) = \frac{1}{5}$ and $P\left( \overline{B} \right) = \frac{1}{4}$
The probability that they contradict each other
$= P(A) \times P\left( \overline{B} \right) + P(\overline{A}) \times P(B)$
$= \frac{4}{5} \times \frac{1}{4} + \frac{1}{5} \times \frac{3}{4}$
$= \frac{1}{5} + \frac{3}{20}$
$= \frac{7}{20}$