Sets, Relations & Functions
Set Operations — B−A
nta_pyq_2026_jan
Grade None
Question:
Let $A=\{x:|x^2-10|\leq6\}$ and $B=\{x:|x-2|>1\}$. Then
A\cup B=(-\infty,1]\cup(2,\infty)
B-A=(-\infty,-4)\cup(-2,1)\cup(4,\infty)
A-B=[2,3]
A\cap B=[-4,-2]\cup[3,4]
Step-by-Step Solution
Key Concept: $A$: $-6\leq x^2-10\leq6\Rightarrow4\leq x^2\leq16\Rightarrow A=[-4,-2]\cup[2,4]$. $B=(-\infty,1)\cup(3,\infty)$. $B-A=B\cap A^c$.
$B-A=(-\infty,-4)\cup(-2,1)\cup(4,\infty)$.
Correct Answer: 2