Mathematics
Statement I: An empty set is always a finite set but a finite set may or may not be empty.
Statement II: The cardinal number of a set of the English alphabet is less than 30.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Answer
Statement I: An empty set has 0 elements (a definite number), so it is a finite set. A finite set has a definite number of elements, which may be 0 (empty) or a positive integer (non-empty). So, Statement I is true.
Statement II: The English alphabet has 26 letters, so the cardinal number of a set of the English alphabet is 26, which is less than 30. So, Statement II is true.
Hence, option 3 is the correct option.
Related Questions
Statement I: {2, 3, 4} and {4, 3, 2} are the same sets.
Statement II: In a set, the order of writing the elements does not matter.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Statement I: An empty set, a singleton set and a set of prime numbers are all finite sets.
Statement II: The cardinal number of a set is always non-negative.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Statement I: The cardinal number of the set A = {x | x ∈ N, x2 < 26} is 6.
Statement II: The number of different elements in a finite set is called its cardinal number.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
State which of the given collections are sets:
(i) collection of all poor people of Dhanbad
(ii) collection of all difficult problems in your maths book
(iii) collection of all popular cinema actors of India
(iv) collection of all countries of Asia
(v) collection of four countries of Asia
(vi) collection of three cities of India whose name start with the letter 'J'
(vii) collection of all people in this world over 50 years of age.