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.
If $A \subset B$ and $B \subset C,$ then $A \subset C$
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.
If $A \subset B$ and $B \subset C,$ then $A \subset C$
True
Let $A \subset B$ and $B \subset C$
Let $x \in A$
$\Rightarrow x \in B \quad[\because A \subset B]$
$\Rightarrow x \in C \quad[\because B \subset C]$
Similar Questions
Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$
$\varnothing$
Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$
$\varnothing$
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
- [KVPY 2012]
The set $A = \{ x:x \in R,\,{x^2} = 16$ and $2x = 6\} $ equals
The set $A = \{ x:x \in R,\,{x^2} = 16$ and $2x = 6\} $ equals
Which of the following are sets ? Justify your answer.
A collection of most dangerous animals of the world.
Which of the following are sets ? Justify your answer.
A collection of most dangerous animals of the world.
The number of non-empty subsets of the set $\{1, 2, 3, 4\}$ is
The number of non-empty subsets of the set $\{1, 2, 3, 4\}$ is