Question

If A = {0,1,2,-1}, then find AxA​

Answer 1

Answer:

given down

Step-by-step explanation:

WE KNOW THAT,

A = {-1,0,1}

TO FIND A X A,

= {-1,0,1} X {-1,0,1}

= {(-1,0,1)} * {(-1,0,1)}=(−1,0,1)∗(−1,0,1)

={(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)}

={(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)}=(−1,−1),(−1,0),(−1,1),(0,−1),(0,0),(0,1),(1,−1),(1,0),(1,1)

Answer 2

A × A = {(0,0) , (0,1) , (0,2) , (0, - 1) , (1,0) , (1,1) , (1,2) , (1, - 1) , (2,0) , (2,1) , (2,2) , (2, - 1) , ( - 1 ,0) , ( - 1 ,1) , ( - 1 ,2) , ( - 1 , - 1)}

Given :

A = {0,1,2,-1}

To find :

The set A × A

Concept :

Cartesian product :

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

Solution :

Step 1 of 2 :

Write down the given set

Here the given set is A = {0,1,2,-1}

Step 2 of 2 :

Find the set A × A

$\sf{A \times A}$

$\sf{ = \{(x, y) : x \in A \: \: and \: \: y \in A \}}$

= {(0,0) , (0,1) , (0,2) , (0, - 1) , (1,0) , (1,1) , (1,2) , (1, - 1) , (2,0) , (2,1) , (2,2) , (2, - 1) , ( - 1 ,0) , ( - 1 ,1) , ( - 1 ,2) , ( - 1 , - 1)}

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