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

Accepted Answer

Determine whether the given information is sufficient to always conclude that every element of set A is also an element of set C.
 {green}	extbf{Answer: True}|||	extbf{Reason: The subset relation is always transitive. Therefore, A $\subset$ C.}{/green} Prove that any element of set A is also an element of set C.
 {green}	extbf{Proof:}|||	extbf{Let x $\in$ A. Since A $\subset$ B, we have x $\in$ B. Since B $\subset$ C, we have x $\in$ C.}|||	extbf{Therefore, every element of A is also an element of C. Hence, A $\subset$ C.}{/green}

Question: 2 (iii)

Answer