Hi,

I've a doubt about his : True or false? : If $\displaystyle \det AB=0$ then $\displaystyle A$ or $\displaystyle B$ is not invertible.

I know that $\displaystyle \det A=0$ or $\displaystyle \det B=0$ but there is also the possible case $\displaystyle \det A$ and $\displaystyle \det B=0$. So I'm tempted to answer False.

Because they say $\displaystyle \{ \text{a proposition} \} \lor \{ \text{another proposition} \}$ while the answer could be $\displaystyle \{ \text{a proposition} \} \land \{ \text{another proposition} \}$. So does the $\displaystyle \lor$ include the $\displaystyle \land$ case?

I know I don't explain myself well. You can answer the question true or false and I will understand. Thank you very much.