Consider the grammar with the following productions.
$$S \to a\,\alpha \,\,b\left| {\,\,b\,\alpha } \right.\,c\,\left| {aB} \right.$$
$$S \to \alpha S\,\left| b \right.$$
$$S \to \alpha \,bb\,\left| {ab} \right.$$
$$S\alpha \to bdb\,\left| b \right.$$
the above grammar is

State whether the following statement is TRUE / FALSE.

A is recursive if both a and its complement are accepted by Turing Machine M accepts.

State whether the following statement is TRUE / FALSE.

The intersection of two $$CFL's$$ is also $$CFL.$$

State whether the following statement is TRUE / FALSE. The problem is to whether a Turing Machine M accepts input $$w$$ is un-decidable.