Which of the following statements is false (w | vedclass

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

Question

(C) The set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$.$1$. $A - B = A \cap B'$ is a standard identity.$2$. $

Vedclass · Accepted Answer

$A - B = A - B'$

Vedclass · Answer

(C) The set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$.$1$. $A - B = A \cap B'$ is a standard identity.$2$. $A - (A \cap B) = A \cap (A \cap B)' = A \cap (A' \cup B') = (A \cap A') \cup (A \cap B') = \emptyset \cup (A \cap B') = A \cap B'$,which is equal to $A - B$.$3$. $(A \cup B) - B = (A \cup B) \cap B' = (A \cap B') \cup (B \cap B') = (A \cap B') \cup \emptyset = A \cap B'$,which is equal to $A - B$.$4$. $A - B'$ is equal to $A \cap (B')' = A \cap B$,which is generally not equal to $A - B$ unless $A \cap B = \emptyset$.Therefore,the statement $A - B = A - B'$ is false.

Which of the following statements is false (where $A$ and $B$ are two non-empty sets)?

Similar Questions

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B - C) =$

In a group of $50$ people, $35$ speak Hindi, $25$ speak both Hindi and English, and all the people speak Hindi or English or both. The number of people who speak English only is

In a certain class,$72 \%$ of the students took Biology and $44 \%$ took Mathematics. If each student took at least one of Biology or Mathematics and $40$ students took both of these subjects,the total number of students in the class is:

If $U = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$,$A = \{3, 5, 7, 11\}$ and $B = \{7, 8, 9, 10, 11\}$,compute $(A - B)'$.

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B \cup C) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module