If U = {1, 2, 3, 4, 5, 6, 7, 8, 9},A = {2, 4, | vedclass

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

Question

Given $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$,and $B = \{2, 3, 5, 7\}$.First,find $A \cap B = \{2\}$.Then,$(A \cap B)^{\prime} = U \s

Vedclass · Accepted Answer

Vedclass · Answer

Given $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$,and $B = \{2, 3, 5, 7\}$.
First,find $A \cap B = \{2\}$.
Then,$(A \cap B)^{\prime} = U \setminus \{2\} = \{1, 3, 4, 5, 6, 7, 8, 9\}$.
Next,find $A^{\prime} = U \setminus A = \{1, 3, 5, 7, 9\}$.
Find $B^{\prime} = U \setminus B = \{1, 4, 6, 8, 9\}$.
Then,$A^{\prime} \cup B^{\prime} = \{1, 3, 5, 7, 9\} \cup \{1, 4, 6, 8, 9\} = \{1, 3, 4, 5, 6, 7, 8, 9\}$.
Since $(A \cap B)^{\prime} = \{1, 3, 4, 5, 6, 7, 8, 9\}$ and $A^{\prime} \cup B^{\prime} = \{1, 3, 4, 5, 6, 7, 8, 9\}$,it is verified that $(A \cap B)^{\prime} = A^{\prime} \cup B^{\prime}$.

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$,and $B = \{2, 3, 5, 7\}$,verify that $(A \cap B)^{\prime} = A^{\prime} \cup B^{\prime}$.

Similar Questions

If $U = \{a, b, c, d, e, f, g, h\}$,find the complement of the set $B = \{d, e, f, g\}$.

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $\text{not } B$.

For each positive real number $\lambda$,let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin(\sqrt{n+1}) - \sin(\sqrt{n})| < \lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

If $U = \{a, b, c, d, e, f, g, h\}$,find the complement of the set $C = \{a, c, e, g\}$.

If $A$ and $B$ are two sets,then $A \cap (A \cap B)^c$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module