May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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4-6 Discrete Mathematical Structures
4.4.4 Negation of Compound Statements
In the negation of a compound statement, the logical connective changes from and (∧) to or (∨)
and vice versa. That is,
(a) ∼( p ∨ q) = (∼p) ∧ (∼q)
(b) ∼( p ∧ q) = (∼p) ∨ (∼q)
These laws are known as De Morgan’s laws.
Table 4.5 Truth table of negation of p ∨ q
Column 1 2 3 4 5 6 7
p q
p ∨ q
∼p ∼q (∼p) ∧ (∼q) ∼( p ∨ q)
T T T F F F F
T F T F T F F
F T T T F F F
F F F T T T T
In Table 4.5, the columns 6 and 7 are identical and hence the result (a) is proved.
Table 4.6 Truth table of negation of p ∧ q
Column 1 2 3 4 5 6 7
p q
p ∧ q
∼p ∼q (∼p) ∨ (∼q) ∼( p ∧ q)
T T T F F F F
T F F F T T T
F
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