[Bash] 'set -e' inheritance...???

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       −e    When this option is on, when any command fails (for any of the reasons listed in Section 2.8.1, Consequences of Shell Errors or by  return‐
             ing an exit status greater than zero), the shell immediately shall exit with the following exceptions:

              1. The  failure  of any individual command in a multi-command pipeline shall not cause the shell to exit. Only the failure of the pipeline
                 itself shall be considered.

              2. The −e setting shall be ignored when executing the compound list following the while, until, if, or  elif  reserved  word,  a  pipeline
                 beginning with the !  reserved word, or any command of an AND-OR list other than the last.

              3. If  the exit status of a compound command other than a subshell command was the result of a failure while −e was being ignored, then −e
                 shall not apply to this command.

             This requirement applies to the shell environment and each subshell environment separately. For example, in:

                 set -e; (false; echo one) | cat; echo two

             the false command causes the subshell to exit without executing echo one; however, echo two is executed because  the  exit  status  of  the
             pipeline (false; echo one) | cat is zero.

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#!/bin/bash

set -e

function myf {
    echo "Enter myf"
    false
    echo "Exit myf"
}

echo "Start"
myf
echo "End"



$ ./x.sh
Start
Enter myf


=======================

#!/bin/bash

set -e

function myf {
    echo "Enter myf"
    false
    echo "Exit myf"
}

echo "Start"
myf || true
echo "End"


$ ./x.sh
Start
Enter myf
Exit myf
End


========================

#!/bin/bash

set -e

function myf {
    echo 'myf' >&2
    exit 2
}

function test {
    a=$(myf)
    echo "TEST DONE"
}

a=$(test)
echo "DONE"

$ ./x.sh
myf
DONE


===========================

#!/bin/bash

set -e

function myf {
    echo 'myf' >&2
    exit 2
}

a=$(myf)
echo "TEST DONE"



$ ./x.sh
myf


====================

#!/bin/bash

set -e

function myf {
    echo 'myf' >&2
    false
    echo "myf DONE"
}

a=$(myf)
echo "DONE"



$ ./x.sh
myf
DONE


=======================

#!/bin/bash

set -e

function myf {
    echo 'myf' >&2
    false
    echo "myf DONE"
}

function test {
    a=$(myf)
    echo 'test DONE'
}

a=$(test)
echo "DONE"


$ ./x.sh
myf
DONE