Class 11th Maths Textbook Chapter 1: Sets Exercise 6: Miscellaneous Question 2 (v) 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. (v) If x $\in$ A and A $
ot\subset$ 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: Since A $
ot\subset$ B, some elements of A are not in B. Therefore, knowing that x $\in$ A does not guarantee that x is an element of B. Although the statement may be true in some cases, it is not true in every case.}{/green} Think of an example where x belongs to A but not to B.
 {green}	extbf{Counter example:}|||	extbf{Let A = \{1, 2\}, B = \{2\}, and x = 1.}|||	extbf{Here, x $\in$ A and A $
ot\subset$ B, but x $
otin$ B.}{/green}

Question: 2 (v)

Answer