First slide

Operations on Sets

Question

Let A and B be two sets then
${(A \cup B)}^{c} \cup (A^{c} \cap B) =$

Moderate

A

$A^{c}$
B

$B^{c}$
C

$ϕ$
D

U

Solution

${(A \cup B)}^{c} \cup (A^{c} \cap B)$
$= (A^{c} \cap B^{c}) \cup (A^{c} \cap B)$
$= (A^{c} \cup A^{c}) \cap (A^{c} \cup B) \cap (B^{c} \cup A^{c}) \cap (B^{c} \cup B)$
$= A^{c} \cap [A^{c} \cup (B \cap B^{c})] \cap U$
$= A^{c} \cap (A^{c} \cup ϕ) \cap U$
$= A^{c} \cap A^{c} \cap U = A^{c} \cap U = A^{c}$
or use venn diagram

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App