Using the symbol for element e and ?

Question

{monday} e {xlx is a day of the week} why is that not a true statement?

Answer 1

Note the difference between {monday} and monday.

monday is a day of the week, so monday є {x | x is a day of the week}

However, {monday} is not a day of the week.

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In response to the above, this is a true statement (note that I changed the set to the right of the 'є', so it's different than the one above):

{monday} є { {x} | x is a day of the week}

This shows that a set CAN be an element; however, we still need to be careful about what we say.

Answer 2

Since you are using set notation, a set can not be an element, but only a subset. {Monday} is a subset of {days}.

Answer 3

Because there's a difference between "Monday" and "{Monday}".  Monday is the day of the week.  {Monday} is a SET, whose only element is "Monday".  A SET itself is not a day of the week.  

So:

Monday є {x | x is a day of the week} is true, but

{Monday} є {x | x is a day of the week} is false.