What is the cartesian product of a definite set with a non empty set
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Cartesian product of a non empty set is just an operation between two sets...You can think it as Operation between two numbers...
When you perform operation between two numbers , You always end up with a result..For example 2 x 5 = 10...Here x is a multiplication operation between the numbers 2 and 5...and 10 is the result we get...
There are other operations like Addition,Subtraction,Division for the numbers...
Simillary we have operations for sets Like
Union-U , Intersection , Difference '-' , and Cartesian Product - ' X ' also called Cross Product..
Remeber when you perform operation between numbers you always get a Result which is nothing just a Number...So Exactly the same way...when you perform operations between the sets like Union,Intersection,Difference and Cartesian Produc, You also get a result as a Set....
For example see Uploaded snap...
Operation like union ,Intersection and Difference give a set of elements are One dimesional numbers..but Set of Cartesian Product is the different set than the set we obtain from the operations Union,Intersection and Difference of sets....
The Set we get from Cartesian product actually a set Of elements in Ordered pair..this means elements are not One dimesional, These elements actually lie on two dimesional plane...So we write elemets in ordered pair...For more info and definition See snap...hope this help...
When you perform operation between two numbers , You always end up with a result..For example 2 x 5 = 10...Here x is a multiplication operation between the numbers 2 and 5...and 10 is the result we get...
There are other operations like Addition,Subtraction,Division for the numbers...
Simillary we have operations for sets Like
Union-U , Intersection , Difference '-' , and Cartesian Product - ' X ' also called Cross Product..
Remeber when you perform operation between numbers you always get a Result which is nothing just a Number...So Exactly the same way...when you perform operations between the sets like Union,Intersection,Difference and Cartesian Produc, You also get a result as a Set....
For example see Uploaded snap...
Operation like union ,Intersection and Difference give a set of elements are One dimesional numbers..but Set of Cartesian Product is the different set than the set we obtain from the operations Union,Intersection and Difference of sets....
The Set we get from Cartesian product actually a set Of elements in Ordered pair..this means elements are not One dimesional, These elements actually lie on two dimesional plane...So we write elemets in ordered pair...For more info and definition See snap...hope this help...
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Sumha:
the have not given any elements in the second set.. the first set is definite
you mean first set is an empty set and other one is Non-Empty...
If this is the case...then The cartesian product of these two sets is Empty...represented by symbol Phai..
no.. there is one set with elements {1,2,3} while set B is a non empty set
can u help me in finding the cartesian product of sat A and B
yes i can
but how can you find the cartesian product of these without knowing the elements of other set B...
You can find out the cartesian product untill you know the elements of each set..
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Answer:
let A and B be two sets consider the pair (a ,b) in which the first element is from A and the second from B . Then (a, b) is called an ordered pair .
In an ordered pair the order in which the two elements are written is important .
Thus (a ,b) and (b, a) are different ordered pairs.
Two ordered pairs( a, b) and (c,d) are said to be equal or same if a is equals to c and b is equals to d.
Step-by-step explanation:
Here is your answer
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