If A and B are two events such that $P(A)>0$ and $P(A)+P(B)>1$, then my reference says the following statement is false : $P(B|A)\geq 1-\frac{P(B')}{P(A)}$
My Attempt $$ P(B|A)\geq 1-\frac{P(B')}{P(A)}\implies\frac{P(A\cap B)}{P(A)}\geq\frac{P(A)-1+P(B)}{P(A)}\\ \frac{P(A\cap B)}{P(A)}\geq\frac{P(A)+P(B)-1}{P(A)}\implies \frac{P(A)+P(B)-P(A\cup B)}{P(A)}\geq\frac{P(A)+P(B)-1}{P(A)}\\ P(A\cup B)\leq 1\;\text{ which is true} $$ What is really going wrong here ?
Here is the snapshot: 