x:x is read as
x is such that
x is ...
N contains the list of factors of 18 . A factor is a number or algebraic expression that divides another number or expression evenly, thus no remainder.
Factors of 18 are
1,2,3,6,9 and 18 itself
Thus
1×18=182×9=183×6=18Hence 1,2,3,6,9 and 18 are factors of 18
⇒N={1,2,3,6,9,18}Multiples of 12 are numbers 12 can divide without a remainder (Simply the multiplication of 12). If you don't know the recitation of the multiples, simply add 12 to the preceding numbers to get the subsequent numbers starting from 12.
Multiples of 12
12,12+12=24,24+12=36,36+12=48,48+12=60, 60+12=72,72+12=84,84+12=96,96+12=108,108+12= 120,120+12=132,132+12=144,... ⇒ multiples of 12 are
12,24,36,48,60,72,84,96,108,120,132,144,...⇒M={12,24,36,48,60,72,84,96,108,120,132,144,...}
∩ means intersection. The element(s) which you can find in both sets.
Hence
N∩M should contain element(s) which can be found in both set
N and
M.
From the above, you can see that there is no element that can be found in
N,{1,2,3,6,9,18} and at the same time be found in
M,{12,24,36,48,60,72,84,96,108,120,132,144,...}. Hence the intersection of
N and
M is an empty set
}