DHARM106 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCEConsider another example,
‘I will take the meal “or” I will go’.
Here sense of connective “or” is exclusive-OR. The statement means either ‘I will take
the meal’ or ‘I will go’ but both situations are not simultaneously occurs.
Negation (~)
Connective Negation is used with unary statement mode. The negation of the statement in-
verts its logic sense. That is similar to the introducing “not” at the appropriate place in the
statement so that its meaning is reverse or negate.
Let A be an statement then negation of A is denoted as ~ A (read as “negation of A” or
“not A”) and the truth value of ~ A is reverse to the truth value of A. Fig. 5.5 defines the
meaning of negation.
A ~ A
FT
TF
Fig. 5.5 (Truth table for negation)
For example, the statement,
‘River Ganges is now profane’. ‘G’ (symbolic representation)
Then negation of statement means ‘River Ganges is sacred’ or ‘River Ganges is not
profane now’. That is denoted by symbolic logic ~ G.
Implication (→)
Let A and B are two statements then the statement A → B (read as “A implies B” or “if A then
B”) is an implication statement (conditional statement) and the truth value of A → B is false
only when truth value of B is false; Otherwise it is true. Truth values of implication are speci-
fied in the truth table shown in fig 5.6.
ABA → B
FFT
FTT
TFF
TTT
Fig. 5.6 (Truth table for Implication)
In the implicative statement (A → B), statement A is known as antecedent or predeces-
sor and statement B is known as consequent or resultant.
Example 5.2. Consider the following statements and their symbolic representation,
It rains : R
Picnic is cancelled : P
Be wet : W
Stay at home : S