Que. No. 13
which of the following is the De-Morgans law
A) None
B)-(PAR)= -PV-R, -(PVR)= -p and -R
OCPVP =True, Pand-P= False
OD) PAQ VR) = (PAQ)V(PAR)
Answers
Answer:
The rules can be expressed in English as:
the negation of a disjunction is the conjunction of the negations
the negation of a conjunction is the disjunction of the negations
or
the complement of the union of two sets is the same as the intersection of their complements
the complement of the intersection of two sets is the same as the union of their complements
or
not (A or B) = not A and not B
not (A and B) = not A or not B.
In set theory and Boolean algebra, these are written formally as
{\displaystyle {\begin{aligned}{\overline {A\cup B}}&={\overline {A}}\cap {\overline {B}},\\{\overline {A\cap B}}&={\overline {A}}\cup {\overline {B}},\end{aligned}}}{\displaystyle {\begin{aligned}{\overline {A\cup B}}&={\overline {A}}\cap {\overline {B}},\\{\overline {A\cap B}}&={\overline {A}}\cup {\overline {B}},\end{aligned}}}
where
{\displaystyle A}A and {\displaystyle B}B are sets,
{\displaystyle {\overline {A}}}{\overline {A}} is the complement of {\displaystyle A}A,
{\displaystyle \cap }\cap is the intersection, and
{\displaystyle \cup }\cup is the union.
In formal language, the rules are written as
{\displaystyle \neg (P\lor Q)\iff (\neg P)\land (\neg Q),}\neg (P\lor Q)\iff (\neg P)\land (\neg Q),
and
{\displaystyle \neg (P\land Q)\iff (\neg P)\lor (\neg Q)}\neg (P\land Q)\iff (\neg P)\lor (\neg Q)
where
P and Q are propositions,
{\displaystyle \neg }\neg is the negation logic operator (NOT),
{\displaystyle \land }\land is the conjunction logic operator (AND),
{\displaystyle \lor }\lor is the disjunction logic operator (OR),
{\displaystyle \iff }\iff is a metalogical symbol meaning "can be replaced in a logical proof with".
Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.