$P_1 \vee P_2 $ , $Q_1 \vee Q_2 $ are semi-decidable predicates and $P_2 = \overline{Q_2}$. What can be said about $P_1 \vee Q_1 $?

124 Views Asked by At

We've just started studying the decidability notion in our Algorithms class. So far we've only defined it and went through some examples of problems that fit different cases : decidable, semi-decidable, undecidable. But that's it. On our test today, this question popped up:


Consider the predicates $P_1,P_2,Q_1,Q_2 : R$ $\rightarrow \{0,1\}$ such that $P_1 \vee P_2 $ , $Q_1 \vee Q_2 $ are semi-decidable and $P_2 = \overline{Q_2}$. What can be said about $P_1 \vee Q_1 $?


I looked on the web before coming here, but I don't really understand how to approach this kind of problems. Can anyone help?