Truth table is a table showing a possible combinations of the variables in an expression in symbolic logic and their resulting truth or falsity.
The English word “And” and “Or” correspond (roughly) to logical connectives. Connectives provide a way of joining simple propositions to form complex propositions.
A logical analysis must state exactly how joining propositions by means of a connective affects the truth of the complex propositions so formed.
LOGICAL CONNECTIVES
q
Conjunction (‘And’) Joining two statements, pieces of information
1. p (premises) - Jhon likes mango
q (premises) - Jhon likes orange
p& q (conclusion) - Jhon likes mango and orange ( T )
2. p& q (premises) - Jhon likes mango and orange
p (conclusion) - Jhon likes mango ( T )
3. p (premises) - Jhon likes mango
p& q (conclusion) - Jhon likes mango and orange ( F)
Feedback :
1. (T) Because we can see from the premises that John likes mango, John likes orange so, we can conclude that John likes mango and orange.
(T) Because one can legitimacy conclude for example that John likes mango from the premises John like mango and orange.
(F) Because one cannot draw the conclusion that John likes mango and orange from the premises John likes mango.
Truth Table “And”
|
p
|
q
|
p & q
|
|
John likes mango
(T)
|
John likes orange
(T)
|
John likes mango and orange
(T)
|
|
John likes mango
(T)
|
John likes orange
(F)
|
John likes mango and orange
(F)
|
|
John likes mango
(F)
|
John likes orange
(T)
|
John likes mango and orange
(F)
|
|
John likes mango
(F)
|
John likes orange
(F)
|
John likes mango and orange
(F)
|
q
Disjunction (“or”) is used to show
an alternatives
Truth Table “or”
|
No
|
p
|
q
|
P V q
|
|
1
|
Rina read
(T)
|
Billy wrote
(T)
|
Rina read or
Billy wrote
( T)
|
|
2
|
Rina read
(T)
|
Billy wrote
(F)
|
Rina read or
Billy wrote
( T)
|
|
3
|
Rina read
(F)
|
Billy wrote
(T)
|
Rina read or
Billy wrote
( T)
|
|
4
|
Rina read
(F)
|
Billy wrote
(F)
|
Rina read or
Billy wrote
(F)
|
Feedback :
1.Because the truth values come from the truth values of their constituent simple propositions.
2.The values T and F which appear in truth tables are same values as the assigned to simple proposition in relation to the situation in the world.
3.The values F and T which appear in truth tables are same values as the assigned to simple proposition in relation to the situation in the world.
4.Because they don’t have constituent simple propositions.
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