JEE Main 2020 — Sets And Relations Question with Solution
From: JEE Main 2020 (Online) 3rd September Morning Slot
Question
A = {m R : both the roots of
x2 – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?
Choose an option
Show full solutionCorrect option: D
Step-by-step explanation
(, 3] [5, )
, 3] [5, )
Given B = [3, 5)
Now, let's examine the options.
Option A : A ∩ B = {–3} The intersection of sets A and B would be the set of elements common to both sets. In this case, the only common element is -3. So, option A is true.
Option B : B – A = (–3, 5) The subtraction (or difference) of sets A from B is the set of elements that are in B but not in A. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting A from B would leave an open interval (-3, 5), not including -3 and 5. So, option B is also true.
Option C : A ∪ B = R The union of sets A and B is the set of elements that are in A, or B, or both. Here, A U B would cover all real numbers. So, option C is true.
Option D : A - B = (-∞, -3) ∪ (5, ∞) The subtraction (or difference) of set B from A is the set of elements that are in A but not in B. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting B from A would leave (-∞, -3) U [5, ∞), not including -3 and 5. But according to the convention for writing intervals, it should be (-∞, -3) U (5, ∞). So, option D is not true.
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