DHARMPROPOSITIONAL LOGIC 105Take another example,
Statement (1) : Stuart is an efficient driver (symbolic logic) K
Statement (2) : India is playing with winning spirit (symbolic logic) S
Then the compound statement will be ‘Stuart is an efficient driver “and” India is playing
with winning spirit’. We can also refer the compound statement in symbolic logic as, K ∧ S. In
fact, the combination of statements (1) and (2) are appear unusual but logically they are repre-
sented correctly.
It must also be clear that, the meaning of the connective ‘and’ (in natural language) is
similar to the meaning of logical ‘AND’. Since conjunction is a binary operation s.t. truth val-
ues of K ∧ S and of S ∧ K are same (from the previous example). Then, the word ‘and’ of natural
language must have the similar meaning.
Consider another example,
‘I reach the station late “and” train left’.
Here conjunction ‘and’ is used in true sense of ‘then’ because one statement performs
action followed by another statement action. So, the true sense of the compound statement is,
‘I reach the station late “then” train left’.
So, readers are given advice to clearly understand the meaning of connective ‘and’.
Disjunction (OR/∨)
Let A and B are two statements then disjunction of A and B is denoted as A ∨ B (read as “A Or
B”) and the truth value of the statement A ∨ B is true if the truth value of the statement A or
B or both are true. Otherwise it is false.
These conditions of the conjunction are specified in the truth table shown in Fig. 5.4.
Disjunction may have more than two statements and by definition it returns truth value
true if truth value of any of the statement is true.
ABA ∨ B
FFF
FTT
TFT
TTT
Fig. 5.4 (Truth table for disjunction)
However the meaning of disjunction is logical ‘OR’ that is similar to the meaning of
connective “or” of natural language. In the next example we see the meaning of disjunction is
‘inclusive-OR’ (not ‘exclusive-OR).
For example, consider a composite statement-
‘Nicolas failed in university exam “or” he tells a lie’.
Here the connective “or” is used as its appropriate meaning. That is, either ‘Nicolas
failed in university exam’ or ‘he tells a lie’ or both situation occurs ‘Nicolas failed in univer-
sity exam’ and also ‘he tells a lie’. Equivalently, we represent above statement by symbolic
logic N ∨ T. (where symbol ‘N’ stands for Nicolas failed in university exam; and symbol ‘T’
stands for he tells a lie)