# Safety property vs Liveness property

If i take a safety property $$SP$$ and a liveness property $$LP$$, is it true that the result of their intersection is a safety property (and not a liveness property) ? Why ?

Thanks

• There are a couple of non-equivalent definitions for liveness properties. What are your precise definitions? – Shaull Aug 20 '19 at 6:32
• "the good thing will happen" – AleWereWolf Aug 20 '19 at 9:00
• Do you mean to say that $L$ is a liveness property if for every finite word $x$, there exists a suffix $y$ such that $xy\in L$? – Shaull Aug 20 '19 at 10:39