The probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is 

Consider the following events:

$E = A$Speaks Truth, $, F = B$ Speaks Truth

We have $P\left(E\right)=\frac{4}{5}$ and $P\left(F\right)=\frac{3}{4}$

Required probability = $\begin{array}{l}= P\left(\right(E\cap \overline{F})\cup (\overline{E}\cap F\left)\right)\\ = P(E\cap \overline{F})+P(\overline{E}\cap F)\\ = P\left(E\right)P\left(\overline{F}\right)+P\left(\overline{E}\right)P\left(F\right)\\ = \frac{4}{5}\times \left(1-\frac{3}{4}\right)+\left(1-\frac{4}{5}\right)\times \frac{3}{4}=\frac{7}{20}\end{array}$