If x is a subset of Y then, is inverse of x also a subset of Y?

Let $ f : X \rightarrow Y $ be a function. If B is subset of y then its inverse image $ f^-B $ is the subset of x define by $ f^-B = {x : f(x) \in B} $ Now prove the following. $ i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1 $ […]

If x belongs to the domain then does f(x) belong to the range?

Let $ F : x \Rightarrow y $ be a function. Then prove that $i. A_1 \subset A_2 \Rightarrow F(A_1) \subset F(A_2)$ $ii. F(\cup_i A_i) = \cup_i F(A_i) $ $iii.F(\cap_i A_i) \subset \cap_i f(A_i)$ Solution $ Let \ f: x \rightarrow y $ be a function. i. $Let\ y \in f(A_1)$ $Then\ \exists x \in […]

Is the empty set a subspace of every vector space? Justify

Question: a. Is the empty set a subspace of every vector space ? Justify and let s = ${(a, b, (a + b):a, b \in R)}$ . Is a subspace of $R^3$ under the usual operation. Question: b. Let I = (-a , a) a > 0 be an open interval in R let v […]

Writing a Linear Regression Class from Scratch Using Python

Linear Regression Introduction Before there was any ML algorithms, there was a concept and that was regression. Linear Regression is considered as the process of finding the value or guessing a dependent variable using the number of independent variables. Take for a example:- predicting a price of house using variables like, size of house, age […]

Scroll to top
Subscribe to our Newsletter

Hello surfer, thank you for being here. We are as excited as you are to share what we know about data. Please subscribe to our newsletter for weekly data blogs and many more. If you’ve already done it, please close this popup.

No, thank you. I do not want.
100% secure.