when we multiply a non empty set with a empty set why does it become a null set - Maths - Relations and Functions

Question

when we multiply a non empty set with a empty set why does it
become a null set ???

Neha Sethi · Accepted Answer

Dear student
We know that the cartesian product  of two sets  A and B is  given by:A×B=a,b:a∈A,b∈BSo  if one of the sets  say A is empty there is no  element a∈A
Hencethere is no element for the ordered pair a,b either
So, ϕ×B=ϕ
Regards

when we multiply a non empty set with a empty set why does it become a null set ???