In bash script
if [ 1 ]
then
echo \"Yes\"
else
echo \"No\"
fi
Output: Yes
It
In unix land, 0 is true and 1 is false.
For your first example:
if [ 1 ]
then
echo "Yes"
else
echo "No"
fi
"If" checks the exit code of the given command for true/false (i.e. zero/non-zero).
The square brackets actually invoke the "test" command (see "man test" for more information) and give the exit code to if.
"test 1" (or indeed "test any_string") returns true (0) so "Yes" is output.
For your second example, this outputs "No" because "nuxi" isn't found in "Linux", if you change "nuxi" to "nux" (perhaps this was a typo?) and remove the spaces around the = then you will get the behaviour you expect. e.g.
word=Linux
letter=nux
if echo "$word" | grep -q "$letter"
then
echo "Yes"
else
echo "No"
fi