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

In a class of $50$ students,$35$ opted for Mathematics and $37$ opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).

Find the cardinal number of the following set $\{x: x\}$ is a natural number $\leq 30$ and is divisible by $7$ or $\{11\}$

If ${N_a} = \{ an : n \in N \} ,$ then ${N_3} \cap {N_4} = $

The range of $f(x) = \sec \left( \frac{\pi}{4} \cos^2 x \right)$ for $-\infty < x < \infty$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module