Show that A cup B=A cap B implies A=B. | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let $a \in A.$ Then $a \in A \cup$ $B$. Since $A \cup B=A \cap B, a \in A \cap B$.

So $a \in B$

Therefore, $A \subset$ $B.$ Similarly, if $b \in

Vedclass · Accepted Answer

Vedclass · Answer

Let $a \in A.$ Then $a \in A \cup$ $B$. Since $A \cup B=A \cap B, a \in A \cap B$.

So $a \in B$

Therefore, $A \subset$ $B.$ Similarly, if $b \in B$, then $b \in A \cup$ $B.$ 

Since $A \cup B=A \cap B, b \in A \cap B .$ So, $b \in A .$

Therefore, $B \subset A .$ Thus, $A=B$

Show that $A \cup B=A \cap B$ implies $A=B$.

Similar Questions

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$\left( {A \cap B} \right) \cap \left( {B \cup C} \right)$

$A-(A-B)$ is

Given the sets $A = \{ 1,\,2,\,3\} ,\,B = \{ 3,4\} , C = \{4, 5, 6\}$, then $A \cup (B \cap C)$ is

Find the union of each of the following pairs of sets :

$A = \{ x:x$ is a natural number and $1\, < \,x\, \le \,6\} $

$B = \{ x:x$ is a natural number and $6\, < \,x\, < \,10\} $

If $A=\{x \in R:|x|<2\}$ and $B=\{x \in R:|x-2| \geq 3\}$ then