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

Accepted Answer

Determine whether the given information is sufficient to always conclude that set A is not a subset of set C.
 {green}	extbf{Answer: False}|||	extbf{Reason: The fact that A $
ot\subset$ B means that some element of A is not in B. Similarly, B $
ot\subset$ C means that some element of B is not in C. These facts do not prevent A from still being a subset 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, 4\}, B = \{1, 2\}, C = \{1, 4, 5\}.}|||	extbf{Here, A $
ot\subset$ B and B $
ot\subset$ C, but A $\subset$ C.}{/green}

Question: 2 (iv)

Answer