JEE Main202225 Jun 2022Evening ShiftMathematicsBasics of MathematicsActual
Let A = x ∈ R : x + 1 < 2 and B = x ∈ R : x - 1 ≥ 2 . Then which one the following statements is NOT true?
Options
- AA - B = - 1 , 1
- BB - A = R - - 3 , 1
- CA ∩ B = ( - 3 , - 1 ]
- DA ∪ B = R - [ 1 , 3 )
Correct answer
B. B - A = R - - 3 , 1
Step-by-step solution
Given, A = x ∈ R : x + 1 < 2 ⇒ A = - 3 , 1 Now, B = x ∈ R : x - 1 ≥ 2 ⇒ B = ( - ∞ , - 1 ] ∪ [ 3 , ∞ ) Now, B - A = ( - ∞ , - 3 ] ∪ [ 3 , ∞ ) ⇒ B - A = R - - 3 , 3 So, option B is not true.