Practicing Success
Practicing Success
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Which of the following sets is not finite? |
$\{(x, y): x^2 + y^2 ≤ 1≤x+y, x, y ∈ R\}$ $\{(x, y): x^2 + y^2 ≤1 ≤ x + y, x, y ∈ Z\}$ $\{(x, y): x^2 ≤ y ≤ |x|, x, y ∈ Z\}$ $\{(x, y): x^2 + y^2 = 1, x, y ∈ Z\}$ |
$\{(x, y): x^2 + y^2 ≤ 1≤x+y, x, y ∈ R\}$ |
The set $\{(x, y): x^2 + y^2 ≤1≤x+y, x, y ∈ R\}$ consists of all point in the first quadrant which lie inside the circle $x^2 + y^2 = 1$ and above the line $x + y = 1$. So, it is not a finite set. We have, $\{(x, y): x^2 + y^2 ≤1≤x+y, x, y ∈ R\} = \{(1, 0), (0, 1)\}$. So, it is a finite set. Clearly, $\{(x, y): x^2 ≤ y ≤ |x|, x, y ∈ Z\} = \{(0, 0), (1, 1), (-1, 1)\}$ which is a finite set. We have, $\{(x, y): x^2 + y^2 = 1, x, y ∈ Z\} = \{(1, 0), (0, 1), (-1, 0), (0, -1)\}$ which is a finite set. |
