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
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 ?
$\{\varnothing\} \subset A$
Are the following pair of sets equal ? Give reasons.
$A = \{ x:x$ is a letter in the word ${\rm{FOLLOW }}\} $
$B = \{ y:y$ is a letter in the word $WOLF\} $
Are the following pair of sets equal ? Give reasons.
$A = \{ x:x$ is a letter in the word ${\rm{FOLLOW }}\} $
$B = \{ y:y$ is a letter in the word $WOLF\} $
List all the subsets of the set $\{-1,0,1\}.$
List all the subsets of the set $\{-1,0,1\}.$
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$A, \ldots B$
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$A, \ldots B$
The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is
The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is