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 ?
$\{1,2,5\}\in A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\in A$
How many elements has $P(A),$ if $A=\varnothing ?$
How many elements has $P(A),$ if $A=\varnothing ?$
If a set $A$ has $n$ elements, then the total number of subsets of $A$ is
If a set $A$ has $n$ elements, then the total number of subsets of $A$ is
Write the following intervals in set-builder form :
$\left[ {6,12} \right]$
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$\left[ {6,12} \right]$
Let $A=\{a, e, i, o, u\}$ and $B=\{a, b, c, d\} .$ Is $A$ a subset of $B ?$ No. (Why?). Is $B$ a subset of $A ?$ No. (Why?)
Let $A=\{a, e, i, o, u\}$ and $B=\{a, b, c, d\} .$ Is $A$ a subset of $B ?$ No. (Why?). Is $B$ a subset of $A ?$ No. (Why?)