mathematics question help Cartesian product of X x Y?

Question

the cartesian product X x Y is given in each of the following part. find X and Y.

a. {(b,c),(c,c)}
b. {(2,1)(2,2),(2,3),(5,1),(5,2),(5,3)}

please help and explain if possible

I am taking Mathematics for elementary teachers and this question was a little tricky for me.But now I understood it really well
Its really hard for me to i\pick the best answer so i;ll let the viewers vote for it. Once again thank you sooooooooooo much for explaining me !

Answer 1

Cartesian product is a set that contains (x,y) with x in X and y in Y

a. {(b,c),(c,c)} so look at the first letter in each set that would be your x and the second y. so in this case x = b,c and y = c,c
therfore X = {b,c} and Y = {c}

b. this is similar to (a): X = {2,5} and Y= {1,2,3}

note: just make sure to seperate the x's and y's, if there is the same number more that once consider it only once like in (b)

hopefully that helped

Answer 2

A Cartesian product is just the set of all possible points that can be combined from the sets.

a) {(b,c),(c,c)} - Now we have to figure out the product in reverse. First we will find X. In the given set we are only going to consider the first value of each sub set. In this case, it is b and c. Therefore X={b,c}. To find Y we are only going to consider the 2nd values for each subset (without repetition). In this case there is only one value, c, so Y={c}.

b) This will work exactly the same as the first problem [except I think you problem was cut off]. I will assume that the given set is supposed to be {(2,1),(2,2),(2,3),(5,1),(5,2),(5,3)}. First we will start by finding X. We will only consider the first numbers of each subset (without considering repitition). The only two numbers are 2 and 5. Therefore X={2,5}. To find Y we will only consider the second numbers given in each subset. In this case the numbers are 1,2,and3. Therefore Y={1,2,3}.

I am currious though, what class you are taking? I have never encountered this before.
b)

Answer 3

Mir, let me first explain to you what Cartesian Product means. Suppose we have 2 sets: A={a,b,c}, &, B={d,e,f,g}. Then the Cartesian Product A x B is defined as the SET of all ordered pairs of the 2 sets A & B. That is, A X B = {(a,d),(a,e),(a,f),(a,g),(b,d),(b,e),.........................(c,f),(c,g)}. Now, one important thing to notice is that in the Cartesian Product, the set of the first elements in each ordered pair forms the set A & the set of the 2nd elements in each ordered pair forms the set B. So, you can notice that A x B is not equal to B x A, as (a,b) is not equal to (b,a).

Now, in (a), the Cartesian Product is given as {(b,c),(c,c)}. Thus, you can find the two sets X & Y whose Cartesian Product is {(b,c),(c,c)} as X={b,c} & Y= {c,c}, or simply, X={b,c} & Y={c}.

Similarly, in (b), you can find out the 2 sets P & Q by inserting all the 1st elements of the Cartesian Product in the set P & all the 2nd elements in the set Q, so that the Cartesian Product is P x Q. Then, P = {2,2,2,5,5,......} & Q = {1,2,3,1,2,.......}, or simply, P={2,5,....} & Q={1,2,3,.....}.

But, note, you can also define the 2 sets as Q ={2,5,....} & P={1,2,3,.....}, but then your Cartesian Product would become QxP.
I hope my answer helps you, Mir. Cheers!

Answer 4

a. (b,c) X=b, Y=c (c,c) X=c, Y=c
b. (2,1) X=2,Y=1 (2,2) X=2,Y=2 (2,3) X=2 Y=3 (5,1) X=5,Y=1
(5,2) X=5, Y=2

Answer 5

better to do it with the help of your teacher.

Sorry beyond limit