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 $A \not\subset B$, 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 $A \not\subset B$, then $x \in B$
False
Let $A=\{3,5,7\}$ and $B=\{3,4,6\}$
Now, $5 \in A$ and $A \not\subset B$
However, $5 \notin B$
Similar Questions
In the following state whether $A=B$ or not :
$A=\{4,8,12,16\} ; B=\{8,4,16,18\}$
In the following state whether $A=B$ or not :
$A=\{4,8,12,16\} ; B=\{8,4,16,18\}$
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
$(i)$ $\{1,2,3,6\}$
$(a)$ $\{ x:x$ is a prime number and a divisor $6\} $
$(ii)$ $\{2,3\}$
$(b)$ $\{ x:x$ is an odd natural number less than $10\} $
$(iii)$ $\{ M , A , T , H , E , I , C , S \}$
$(c)$ $\{ x:x$ is natural number and divisor of $6\} $
$(iv)$ $\{1,3,5,7,9\}$
$(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
| $(i)$ $\{1,2,3,6\}$ | $(a)$ $\{ x:x$ is a prime number and a divisor $6\} $ |
| $(ii)$ $\{2,3\}$ | $(b)$ $\{ x:x$ is an odd natural number less than $10\} $ |
| $(iii)$ $\{ M , A , T , H , E , I , C , S \}$ | $(c)$ $\{ x:x$ is natural number and divisor of $6\} $ |
| $(iv)$ $\{1,3,5,7,9\}$ | $(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $ |
Which of the following are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $
Which of the following are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $
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 $x \notin A$
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 ?
$\{1,2,3\}\subset A$