Consider the following statements: I. The set of all birds living on the Earth is an infinite set. II. The set of all real numbers between 0 and 10 is a finite set. Which of the statements given above is/are correct?
Neither I nor II
The set of all birds living on Earth at any time is a large but finite (countable) population, so statement I is incorrect. The set of all real numbers between \(0\) and \(10\) is uncountably infinite, so statement II is also incorrect. Hence neither statement is correct.
Similar Questions
If A = {x : x is a multiple of 7},
B = {x : x is a multiple of 5} and
C = {x : x is a multiple of 35}
Then which of the following is null set?
Consider the following sets:
I. The set of even prime numbers
II. \(\{x\in\mathbb{R}:x^3+1=0\}\)
III. \(\{n\in\mathbb{Z}:n^2<1\}\)
How many of the above are null sets?
Important Questions from Sets
Consider two subsets of ℝ 2given as, S1 = {[1, -2], [3, 5]} and S2 = {[1, 1], [0, 0]}. Then,
The standard ordered basis of ℝ 2is {e 1, e 2}. Let T : ℝ 2 → ℝ 2 be the linear transformation such that T reflects the points through the line x 1= -x 2. The standard matrix of T is:
In a class, 20 students opted for physics, 17 for Maths, 12 for both physics and maths and 10 students for other subjects. The class contains how many students?
The set N of natural numbers is:
Suppose A1, A2, A3, ..., A30 are thirty sets each having 5 elements with no common elements across the sets and B1, B2, ..., Bn are n sets each with 3 elements with no common elements across the sets. Let \(\rm \displaystyle\bigcup^{30}_{i = 1} A_i = \displaystyle\bigcup^n_{j = 1} B_j = S\) and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to
