Which one of the following is a null set? A = {x : x is prime} B = {x : x + 8 = 8} C = {x : x2 + 1 = 0, x is a real number} D = {x : x2 = 4, x is an integer}
C
Concept:
Empty Set, also known as the null set, is a set that contains nothing. It is represented as { }.
Analysis:
1. The set contains all prime numbers such as 2, 3, 5, etc. Therefore, it is not an empty set.
2. The set has a value of 0, so it is not an empty set.
3. Here, x2 + 1 = 0
⇒ x2 = -1
⇒ x = √-1 (which is not real)
Butx ϵ R, therefore this set is an empty set
Thus, option (1) is correct.
4. The set includes 2, -2. Therefore, it is not an empty set.
Important Questions from Operations on Sets
What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?
If A = {x ∈ R : x 2+ 6x - 7 < 0} and B = {x ∈ R : x 2+ 9x + 14 > 0}, then which of the following is/are correct?
1. (A ∩ B) = (-2, 1)
2. (A - B) = (-7, -2)
Select the correct answer using the code given below:A, B, C and D are four sets such that A ∩ B = C ∩ D = ϕ. Consider the following:
1. A ∪ C and B ∪ D are always disjoint.
2. A ∩ C and B ∩ D are always disjoint.
Which of the above statements is/are correct?A coin is tossed three times. Consider the following events:
A: No head appears
B: Exactly one head appears
C. At least two heads appear
Which one of the following is correct?
If C = { 2, 4, 6, 8, 10, 12, 14, 16 }, and D = {5, 10, 15, 20}, then the number of elements in the set D - C is:
