Does $a match the regex pattern in $b?

$a =~ /$b/
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Does $a contain the string in $b?

$a =~ /\Q$b\E/

$a =~ /\Q$b/  # \E is optional

my $b_re = quotemeta($b);  # This is what \Q does
$a =~ /$b_re/
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Does $a equal the string in $b?

$a eq $b

$a =~ /^\Q$b\E\z/

my $b_re = quotemeta($b);
$a =~ /^$b_re\z/
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quotemeta