Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = =
P(B) = =
P(A &minus ;lie) = 1 − =
P(B − lie) = 1 − =
Now
A and B contradict each other = [A lies and B true] or [B true and B lies]
= P(A).P(B − lie) + P(A − lie).P(B)
[Please note that we are adding at the place of OR]
= ( × ) +( × ) =
= ( × 100) % = 35%