Computer-Networks
March 27, 2024Question 11511 – APPSC-2012-DL CA
March 27, 2024Question 11508 – APPSC-2012-DL CA
If A, B, and C are subsets of U then the simplified form of the expression ~A∪~B∪(A∩B∩~C) using the law of set theory is
Correct Answer: B
Question 38 Explanation:
A’∪B’∪(A∩B∩C’)
In general we can write it as,
A’ + B’ + (ABC’)
= A’ + B’ + ABC’
= A’ + (B’ + B)(B’ + AC’)
= A’ + 1∙(B’ + AC’)
= A’ + B’ + AC’
= (A’ + A)(A’ + C’) + B’
= A’ + C’ + B’
= A’∪C’∪B’
= A’∪B’∪C’
In general we can write it as,
A’ + B’ + (ABC’)
= A’ + B’ + ABC’
= A’ + (B’ + B)(B’ + AC’)
= A’ + 1∙(B’ + AC’)
= A’ + B’ + AC’
= (A’ + A)(A’ + C’) + B’
= A’ + C’ + B’
= A’∪C’∪B’
= A’∪B’∪C’
~A∩~B∩~C
~A∪~B∪~C
~A∪~B∪C
~A∩~B∪~C