Class 11th Maths Textbook Chapter 1: Sets Exercise 6: Miscellaneous Question 2 (ii) 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. (ii) If A $\subset$ B and B $\in$ C, then A $\in$ C

Accepted Answer

Determine whether the given information is sufficient to always conclude that set A is an element of set C.
 {green}	extbf{Answer: False}|||	extbf{Reason: The fact that A $\subset$ B means that every element of A is also an element of B. The fact that B $\in$ C only means that set B is an element of C. These facts do not imply that A must also be an element of C. 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 C = \{\{1, 2\}, 3\}.}|||	extbf{Here, A $\subset$ B, B $\in$ C, but A $
otin$ C}{/green}

Question: 2 (ii)

Answer