Consider the following languages

A$^\{\backslash$forall$\}=\backslash$left$\backslash \{|$M$\backslash \backslash$text$\{$is a TM that accepts all strings of length less than k$\}\backslash$right$\backslash \}$

and

A$^\{\backslash$exists$\}=\backslash$left$\backslash \{|$M$\backslash$text$\{$ is a TM that accepts some strings of length less than k$\}\backslash$right$\backslash \}$

Note the difference between the languages all strings vs some strings

$1)$To show a language L is Turing$-$recognizable, we need to build a TM that behaves as follows:

TM on input w:

The TM accepts if

$.$

TM rejects or loop if

To show a language L is Turing$-$recognizable, we need to build a TM that behaves as follows:

TM on input w:

The TM accepts if w$\backslash$in L$.$

TM rejects or loop if w

otin L

True

False