Let A = {(α,β) ∈ R × R : |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = {(α,β) ∈ R × R : 16(α - 2)^2 + 9(β - 6)^2 ≤ 144}. Then (1) B ⊂ A (2) A ∪ B = {(x,y) : -4 ≤ x ≤ 4, -1 ≤ y ≤ 11} (3) Neither A ⊂ B nor B ⊂ A (4) A ⊂ B

Question

Accepted Answer

B ⊂ A. The correct option is right because the set B, defined by an ellipse, is entirely contained within the rectangular bounds of set A, which encompasses a larger area defined by the inequalities |α - 1| ≤ 4 and |β - 5| ≤ 6.

Let A = {(α,β) ∈ R × R : |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = {(α,β) ∈ R × R : 16(α - 2)^2 + 9(β - 6)^2 ≤ 144}. Then (1) B ⊂ A (2) A ∪ B = {(x,y) : -4 ≤ x ≤ 4, -1 ≤ y ≤ 11} (3) Neither A ⊂ B nor B ⊂ A (4) A ⊂ B

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