The probability of speaking truth by A, P(A) = $${4 \over 5}$$. The probability of not speaking truth by A, P($$\overline A $$) = 1 $$-$$ $${4 \over 5} = {1 \over 5}$$.

The probability of speaking truth by B, P(B) = $${3 \over 4}$$. The probability of not speaking truth of B, P($$\overline B $$) $$ = {1 \over 4}$$.

The probability that they contradict each other

$$ = P(A) \times P(\overline B ) + P(\overline A ) \times P(B)$$

$$ = {4 \over 5} \times {1 \over 4} + {1 \over 5} \times {3 \over 4}$$

$$ = {1 \over 5} + {3 \over {20}} = {7 \over {20}}$$