enter image description here$A=\{ a,b,c \}$ $B= \{a,c,d\}$
$A\times B=\{ (a,a),(a,c),(a,d),(b,a),(b,c),(b,d),(c,a),(c,c),(c,d)\}$ $B\times A= \{ (a,a),(a,b),(a,c),(c,a),(c,b),(c,c),(d,a),(d,b),(d,c)\}$
i want to intersect this two sets.
$(A \times B) \cap (B \times A)=$ ???
my question is, is $(c,b)$ and $(b,c)$ the same thing? because, if they are same I am going to have the different result in comparison to if they are not same.
If not why?
this is the original question. I am solving b.
On
The answer to your title: Do order of $\require{cancel}\bcancel{\text{compenents}}$ elements in a set matter?
No. A set is an unordered collection of elements. $\{fred,wilma,barney,betty\}=\{betty,wilma, fred,barney\}$ because order does not matter.
The answer to your body: is $(c,b)$ and $(b,c)$ the same thing?
No. $A\times B$ is defined to be a set of ordered pairs. $(c,b)$ is not an unordered set but is an ordered pair. $(c,b) \ne (b,c)$.
No, they are not the same.
By definition, $$(a,b)=(c,d)\iff a=c \wedge b=d$$
and so $(a,b)\not=(b,a)$ for $a\not=b$.