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Which of the following is an empty set?
(A) The set of prime numbers which are even.
(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R
(C) (AB) cap(B* A) where A and B are
disjoint. (D) The set of reals which satisfy
x ^ 2 + ix + 1 - 1 = 0?
(A) The set of prime numbers which are even.
(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R
(C) (AB) cap(B* A) where A and B are
disjoint. (D) The set of reals which satisfy
x ^ 2 + ix + 1 - 1 = 0?
Most Upvoted Answer
Which of the following is an empty set?(A) The set of prime numbers wh...
Identifying the Empty Set
To determine which of the given options represents an empty set, let's analyze each option individually:
(A) The set of prime numbers which are even.
- The only even prime number is 2.
- Therefore, the set is not empty; it contains one element: {2}.
(B) The solution set of the equation 2(2x + 3)x + 1(2x + 1) + 3 = 0, x ∈ R.
- Simplifying this equation is complicated, but we can check for real solutions.
- If the discriminant of the corresponding quadratic equation is negative, there are no real solutions.
- If it turns out that no real solutions exist, this set would be empty.
(C) (A ∩ B) ∩ (B* ∩ A) where A and B are disjoint.
- If A and B are disjoint, then A ∩ B = ∅ (empty set).
- Subsequently, any operation involving an empty set will also yield an empty set.
- Thus, this option is empty: ∅.
(D) The set of reals which satisfy x² + ix + 1 - 1 = 0.
- This simplifies to x² + ix = 0.
- Factoring gives x(x + i) = 0, leading to solutions x = 0 or x = -i.
- Therefore, this set is not empty as it contains complex solutions.
Conclusion:
- From the options analyzed, options (A), (B), and (D) are non-empty.
- Option (C) is an empty set due to the disjoint nature of A and B.
Thus, the correct answer is **(C)**.
To determine which of the given options represents an empty set, let's analyze each option individually:
(A) The set of prime numbers which are even.
- The only even prime number is 2.
- Therefore, the set is not empty; it contains one element: {2}.
(B) The solution set of the equation 2(2x + 3)x + 1(2x + 1) + 3 = 0, x ∈ R.
- Simplifying this equation is complicated, but we can check for real solutions.
- If the discriminant of the corresponding quadratic equation is negative, there are no real solutions.
- If it turns out that no real solutions exist, this set would be empty.
(C) (A ∩ B) ∩ (B* ∩ A) where A and B are disjoint.
- If A and B are disjoint, then A ∩ B = ∅ (empty set).
- Subsequently, any operation involving an empty set will also yield an empty set.
- Thus, this option is empty: ∅.
(D) The set of reals which satisfy x² + ix + 1 - 1 = 0.
- This simplifies to x² + ix = 0.
- Factoring gives x(x + i) = 0, leading to solutions x = 0 or x = -i.
- Therefore, this set is not empty as it contains complex solutions.
Conclusion:
- From the options analyzed, options (A), (B), and (D) are non-empty.
- Option (C) is an empty set due to the disjoint nature of A and B.
Thus, the correct answer is **(C)**.
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Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0?
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Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0?.
Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is an empty set?(A) The set of prime numbers which are even.(B) The solution set of the equation 2(2x+3) x+1 2 x+1 +3=0, x \in R(C) (AB) cap(B* A) where A and B aredisjoint. (D) The set of reals which satisfyx ^ 2 + ix + 1 - 1 = 0?.
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