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प्रश्न
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
Set A = {0, 1, 2} - A is a finite set of 3 integers.
Set B = {x ∈ ℝ | 0 ≤ x ≤ 2} B includes all real numbers from 0 to 2. That means:
B = {x ∈ R ∣ 0 ≤ x ≤ 2}
which includes:
- All whole numbers: 0, 1, 2
- All decimal values: 0.1, 0.5, 1.25, 1.999, etc.
- All irrational values: √2, π/2, etc.
The image wrongly claims that:
B = {0, 1, 2}
That is only true if B is defined as: B = {x ∈ Z ∣ 0 ≤ x ≤ 2}
(where Z = set of integers)
But the question clearly states:
x ∈ R — set of real numbers, not just integers.
So B is an infinite set, while A is a finite set.
Sets A and B are not equal. Hence, the statement is False.
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