Moreover, you should use strict: it would have told you

Bareword "false" not allowed while "strict subs" in use at - line 1.
Bareword "true" not allowed while "strict subs" in use at - line 2.
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The common value used for true is 1, for false, you can use 0, "" or undef.

Also, $a and $b are special variables used in sort, it's better not to use them anywhere else.

#!/usr/bin/perl
use warnings;
use strict;

my $A = 0;
my $B = 1;

print "Value of \$A = $A and value of \$B = $B\n";

my $c = ($A and $B);
print "Value of \$A and \$B = $c\n";

$c = ($A  && $B);
print "Value of \$A && \$B = $c\n";

$c = ($A or $B);
print "Value of \$A or \$B = $c\n";

$c = ($A || $B);
print "Value of \$A || \$B = $c\n";

$A = 0;
$c = not($A);
print "Value of not(\$A)= $c\n";
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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In addition to what choroba said, if you really want to be able to use the keywords true and false in your script, there are a few CPAN modules which will provide them for you, such as boolean. Or you can just define them as constants.

use constant {qw( true 1 false 0 )};
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When did this form become valid? I used on my dev box (5.28) but on production (5.16) I get a syntax error and need to use

use constant {true=>1,false=>0}

Interestingly, it's a difference in Perl parser, not in constant. As usually, help the parser by telling it the { doesn't start a block, but a hash reference:

use constant +{ qw( true 1 false 0 ) };
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map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

perldelta for 5.18.0 says:

use no longer tries to parse its arguments as a statement, making use constant { () }; a syntax error (perl #114222).

which I believe refers to this.

See also Truth and Falsehood in perlsyn for more on truthyness in Perl.

Always use use strict; use warnings qw( all );!!!

Idly wondering why this hasn't become the default ...

We went through all that more than a decade ago: Why isn't C<use strict> the default?

Idly wondering why this hasn't become the default ...

Well, at least there's this: use 5.012; and up enables strict. Backwards compatibility is a big thing with Perl 5, and hence there are often fairly long deprecation cycles for incompatible changes, and if one wants to use the newer features of the new Perl versions, use VERSION; is an easy way to do that.

See also use and feature.