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.
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?
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?
A college awarded 38 medals in Football, 15 in Basketball and 20 in Cricket. If these medals went to a total of 58 men and only 3 men got medals in all the 3 sports, how many received medals in exactly two of the 3 sports?
The set N of natural numbers is: