Assume that $P(A)=P(B) .$ Show that $A=B$.
Assume that $P(A)=P(B) .$ Show that $A=B$.
Let $P(A)=P(B)$
To show: $A=B$
Let $x \in A$
$A \in P(A)=P(B)$
$\therefore x \in C,$ for some $C \in P(B)$
Now, $C \subset B$
$\therefore x \in B$
$\therefore A \subset B$
Similarly, $B \subset A$
$\therefore A=B$
Similar Questions
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$ 2 \, ....... \, A $
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$ 2 \, ....... \, A $
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
$(i)$ $\{ P,R,I,N,C,A,L\} $
$(a)$ $\{ x:x$ is a positive integer and is adivisor of $18\} $
$(ii)$ $\{ \,0\,\} $
$(b)$ $\{ x:x$ is an integer and ${x^2} - 9 = 0\} $
$(iii)$ $\{ 1,2,3,6,9,18\} $
$(c)$ $\{ x:x$ is an integer and $x + 1 = 1\} $
$(iv)$ $\{ 3, - 3\} $
$(d)$ $\{ x:x$ is aletter of the word $PRINCIPAL\} $
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
| $(i)$ $\{ P,R,I,N,C,A,L\} $ | $(a)$ $\{ x:x$ is a positive integer and is adivisor of $18\} $ |
| $(ii)$ $\{ \,0\,\} $ | $(b)$ $\{ x:x$ is an integer and ${x^2} - 9 = 0\} $ |
| $(iii)$ $\{ 1,2,3,6,9,18\} $ | $(c)$ $\{ x:x$ is an integer and $x + 1 = 1\} $ |
| $(iv)$ $\{ 3, - 3\} $ | $(d)$ $\{ x:x$ is aletter of the word $PRINCIPAL\} $ |
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\varnothing \in A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\varnothing \in A$
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\} $