The probabilities of two persons A and B for telling the truth are 4/5 and 3/4 respectively. Find the probability that they contradict each other when asked about same topic ?

You need to add the probabilities that both A and B tell the truth to the probability that both A and B are lying. Do you know how to calculate the probability that both tell the truth? Then, keep in mind that if the probability of a person telling the truth is x, then the probability of his lying is 1 - x, can you then calculate the probability that they are both lying? Add these together, and you have your answer.

suppose probability of A telling the truth is x and B telling the truth is y

Then probability of A lying is (1 -x) and B lying is (1 - y)

Also remember that prabability occurrence of two independent events with probabilities X and Y = XY

The probability of contradiction will be:

(Probablity of A telling the truth and B lying) + (Probablity of B telling the truth and A lying)

Probability of A telling the truth and B lying =
(Probability of A telling the truth) (Prabability of B lying)

Now you should be able to work out.