If A and B are two sets,then A cup B = A cap | vedclass

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

Question

(C) Given $A \cup B = A \cap B$.Let $x \in A$. Since $A \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \i

Vedclass · Accepted Answer

$A = B$

Vedclass · Answer

(C) Given $A \cup B = A \cap B$.Let $x \in A$. Since $A \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \in A \cap B$.By definition of intersection,$x \in A \cap B \Rightarrow x \in A$ and $x \in B$. Thus,$x \in B$.Therefore,$A \subseteq B$.Similarly,let $x \in B$. Since $B \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \in A \cap B$.By definition of intersection,$x \in A \cap B \Rightarrow x \in A$ and $x \in B$. Thus,$x \in A$.Therefore,$B \subseteq A$.Since $A \subseteq B$ and $B \subseteq A$,we conclude that $A = B$.

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if

Similar Questions

Determine whether the following set is finite or infinite:
$\{1, 2, 3, \ldots\}$

Write the following set in roster form:
$B = \{x : x \text{ is a natural number less than } 6\}$

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\{\varnothing\} \subset A$

Examine whether the following statement is true or false:
$\{a\} \subset \{a, b, c\}$

Write the following as an interval: $\{ x : x \in R, -4 < x \le 6 \}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module