Class 11th Maths Textbook Chapter 1: Sets Exercise 6: Miscellaneous Question 2 (i) Solution

Question

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x $\in$ A and A $\in$ B, then x $\in$ B

Accepted Answer

Determine whether the given information is sufficient to always conclude that x is an element of set B.
 {green}	extbf{Answer: False}|||	extbf{Reason: The fact that A $\in$ B only means that set A is an element of B. It does not imply that every element of A must also be an element of B. Therefore, although the statement may be true in some cases, it is not true in every case.}{/green} Think of a simple example to show that the given statement is false.
 {green}	extbf{Counter example:}|||	extbf{Let A = \{1\}, B = \{\{1\}, 2\}, and x = 1.}|||	extbf{Here, x $\in$ A, A $\in$ B, but x $
otin$ B.}{/green}

Question: 2 (i)

Answer