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 $x \notin B,$ then $x \notin A$
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 $x \notin B,$ then $x \notin A$
True
Let $A \subset B$ and $x \notin B$
To show: $x \notin A$
If possible, suppose $x \in A$
Then, $x \in B,$ which is a contradiction as $x \notin B$
$\therefore x \notin A$
Similar Questions
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,3\}\subset A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,3\}\subset A$
How many elements has $P(A),$ if $A=\varnothing ?$
How many elements has $P(A),$ if $A=\varnothing ?$
State whether each of the following set is finite or infinite :
The set of animals living on the earth
State whether each of the following set is finite or infinite :
The set of animals living on the earth
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Write the following sets in roster form :
$A = \{ x:x$ is an integer and $ - 3 < x < 7\} $
Write the following sets in roster form :
$A = \{ x:x$ is an integer and $ - 3 < x < 7\} $