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If $A$ is a set of all $(x,y)$ which belong to $\mathbb{R}\times\mathbb{R}$ and $x^2+y^2=1$ while $B$ is a set of all $(x,y)$ which belong to $\mathbb{R}\times\mathbb{R}$ and $x$ and $y$ both are equal to or greater than $-1$ and equal to or less than $1$ then what are

$$A \cup B,$$ and $$A \cap B?$$

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Remark : I use R² to denote " R cross R" ( the cartesian product of R by itself)

Use symbolab to visualize the sets in question :

https://www.symbolab.com/graphing-calculator

A = { (x,y) belonging to R²| x²+y² = 1}

The set A is the circle of center (O,O) and of radius 1.

B = { (x,y) belonging to R²| x belongs to [-1; 1] and y belongs to [-1;1] }

The set B is the area enclosed in the parallel vertical lines x=1, x=-1, and the parallel horizontal lines y=-1 and y=1. I let you determine what is this area and in which figure it is enclosed.

A Union B = { (x,y) belonging to R²| x²+y² = 1 OR x and y belong to [-1; 1] }

A Union B is the set of all points ( x, y) that belong to the circle OR to the aforementionned area ( or to both of them). Remark : in the definition of " union" the " or" is the inclusive or ( inclusive disjunction).

A Inter B = { (x,y) belonging to R²| x²+y² = 1 AND x and y belong to [-1; 1] }

A Inter B is the set of points (x,y) that belong both to the circle and to the aforementionned area .

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    $\begingroup$ Thanks for giving the solution $\endgroup$ – Girish chandra May 17 at 0:58

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