We have the following sets:
M = {2,4,6,8,10,12,14}
N = {x ∈R|x>1 ∧ x is a divisor of 180 ∧ x<15}
L = {1,2,3,5,8,13,21}
and the following statement:
{} ∉ M ∩(N ×L)
Is the statement true or false?
Let R = M ∩(N ×L)
R = {}
So an empty set is an element of R={}?
Therefore the statement is false?
Since $R = \{\}, \{\} \not \in R$, because $\{\} \not \in \{\}$. Otherwise $R$ would not be empty, but $R$ would be $ = \{\{\}\}$.
Imagine sets as boxes:
$\{ \}$ is an empty box - a box with nothing in it.
$\{ \} \in A$ would mean that there is an empty box inside the box $A$ - but then $A$ is not empty, but contains something, namely a box.
$\{\{\}\}$ is not an empty box: It is a box that contains one thing, namely an empty box. And obviously a box with an (empty) box in it is not the same as an empty box.
So if $R = \{\}$, then $R$ is a box that contains nothing, not even an empty box, and therefore $\{\} \not \in \{\}$.