markvillalon19300

2022-09-18

๐={๐โโค|๐=1+(โ1)๐,for some ineteger ๐}

To solve the given set equation:

We can break down the equation and determine the elements that satisfy the condition.
The equation states that T is the set of integers m, such that m can be expressed as $1+\left(โ1\right)i$, where i is an integer.
Let's examine the expression $1+\left(โ1\right)i$ for different values of i:
For i = 0: $1+\left(โ1\right)\mathrm{ยท}0=1+0=1$
For i = 1: $1+\left(โ1\right)\mathrm{ยท}1=1โ1=0$
For i = 2: $1+\left(โ1\right)\mathrm{ยท}2=1โ2=โ1$
For i = 3: $1+\left(โ1\right)\mathrm{ยท}3=1โ3=โ2$
...
Based on these calculations, we can see a pattern emerging. The expression $1+\left(โ1\right)i$ alternates between 1 and 0 as i increases. In other words, for every even value of i, the expression evaluates to 1, and for every odd value of i, it evaluates to 0.
Therefore, we can express the set T as:

In set notation, this can be written as:
$T=\left\{1,0\right\}$
Thus, the solution to the set equation is $T=1,0$.

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