Sets & Set Theory Q&A Archives - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day

Determine whether each of these functions is a bijection from R to R.

$f(x)= −3x+4$ $f(x)= −3(x)^2+7 $ $f(x)= dfrac{x+1}{x+2}$ $f(x)= (x)^5 + 1$ This question aims to find which of the above-mentioned functions is a bijection from R to R. A bijection is also known as a bijective function or one-to-one correspondence. A function is called a bijective function if it fulfills the conditions of both the […]

Find two sets A and B such that A ∈ B and A ⊆ B.

In this question, we have to find two Sets that fulfill the given condition in the question statement which are $ A in B $ and also $ Asubseteq B $ The basic concept behind this question is the understanding of Sets, Subsets, and Elements in a Set. Read moreThe domain of every Rational function […]

At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]

The domain of every Rational function is the set of all Real numbers.

This question aims to find whether the domain of all the rational numbers is a set of all real numbers or not. We have to find whether this statement is true or false. Any number that exists in the world and that can be seen falls in the category of real numbers. Real numbers include […]