Let $L_1,L_2$ be two languages and HALT the language defined in the lecture about the halting problem. Which of the following is true:

a$.$ If $L_1$ and $L_2$ are Turing recognizable, then the set difference $L_1-L_2$ is Turing recognizable

b$.$ Assume $L_1$ is not TM recognizable. Then the union of $L1$ with any other language is not recognizable.

c$.$ If $L_1$ and $L_2$ are Turing recognizable, then the set union $L_1{L}_2$ is Turing recognizable

d$.$ If $L_1$ and $L_2$ are Turing recognizable, then the concatenation $L_1{L}_2$ is not necessarily Turing recognizable