Mathematics · Sets and Relations

Let A = {x ∈ ℝ : ⌊x + 3⌋ + ⌊x + 4⌋ ≤ 3} and B = {x ∈ ℝ : 3x (∑r=1∞ 310r)x - 3 < 3-3x}, where ⌊·⌋ denotes the greatest integer function. Then:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1A ∩ B = ∅
2A = B✓
3B ⊂ A, A ≠ B
4A ⊂ B, A ≠ B

Correct answer

A = B

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Let A = {x ∈ ℝ : ⌊x + 3⌋ + ⌊x + 4⌋ ≤ 3} and B = {x ∈ ℝ : 3x (∑r=1∞ 310r)x - 3 < 3-3x}, where ⌊·⌋ denotes the greatest integer function. Then:

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Let A = {x ∈ ℝ : ⌊x + 3⌋ + ⌊x + 4⌋ ≤ 3} and B = {x ∈ ℝ : 3x (∑r=1∞ 310r)x - 3 < 3-3x}, where ⌊·⌋ denotes the greatest integer function. Then:

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