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 $x \in A$ and $A \in B,$ then $x \in B$
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 $x \in A$ and $A \in B,$ then $x \in B$
False
Let $A=\{1,2\}$ and $B=\{1,\{1,2\},\{3\}\}$
Now, $2 \in\{1,2\}$ and $\{1,2\}$ $\in\{\{3\}, 1,\{1,2\}\}$
$\therefore A \in B$
Howerer, $2 \notin\{\{3\}, 1,\{1,2\}\}$
Similar Questions
From the sets given below, select equal sets:
$A=\{2,4,8,12\}, B=\{1,2,3,4\}, C=\{4,8,12,14\}, D=\{3,1,4,2\}$
$E=\{-1,1\}, F=\{0, a\}, G=\{1,-1\}, H=\{0,1\}$
From the sets given below, select equal sets:
$A=\{2,4,8,12\}, B=\{1,2,3,4\}, C=\{4,8,12,14\}, D=\{3,1,4,2\}$
$E=\{-1,1\}, F=\{0, a\}, G=\{1,-1\}, H=\{0,1\}$
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an even natural mumber $\} \ldots \{ x:x$ is an integer $\} $
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an even natural mumber $\} \ldots \{ x:x$ is an integer $\} $
Which of the following are examples of the null set
Set of even prime numbers
Which of the following are examples of the null set
Set of even prime numbers
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{\varnothing\} \subset A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{\varnothing\} \subset A$
Write the following intervals in set-builder form :
$\left( { - 3,0} \right)$
Write the following intervals in set-builder form :
$\left( { - 3,0} \right)$