$)$ If during a computation a Turing Machine enters the same configuration twice,

then the Turing Machine will loop $($never reach the accept or reject state$).$

$($b$)$ If a Turing Machine loops, then there exists a configuration that the Turing

Machine enters at least twice.

$($c$)$ The language L$=\{$M $|$M $$ is a Turing Machine that accepts a palindrome$\}$

is decidable.

$($d$)$ The language L$=\{$M $|$M $$ is a Turing Machine that accepts a palindrome$\}$

is recognizable.

$($e$)$ If languages A and B are decidable, then their union A $$ B is decidable.

$($f$)$ If languages A and B are recognizable, then their union A $$ B is recognizable.

$($g$)$ If languages A and B are decidable, then their set$-$difference A $\backslash$ B is decidable.

$($h$)$ If languages A and B are recognizable, then their set$-$difference A $\backslash$ B is recogniz$-$

able.

$($i$)$ For every language A that is not recognizable, the complement AC is recognizable.

$($j$)$ The set of all finite tuples of natural numbers S$=\{($x$1,$ x$2,...,$ xk$)|$ xi in N$,$ k in

N$\}$ is countable.