Topic : Find the truth values of the conjunction,
disjunction, implication, bi-implication, converse,
contrapositive and inverse.
By
Sangeeta Panda : 220301230011
Sec : D
Branch : B.Tech - Aerospace
Guided by
MR.Sasi Bhusan Padhi
Introduction to Proposition:
Proposition is a declarative sentence(a sentence that is declaring a fact or
stating an argument) which can be either TRUE or FALSE but cannot be both.
For example:
Delhi is the capital of India
Rose is a flower.
4+5=9
Note:
All Exclamatory sentences, Question sentences, Order sentences, and
sentences that contain undefined words like good, bad, excellent and which
contains variables like x, y, z, u, v,….etc are not propositions.
For example:
Oh! What a beautiful place it is.
What time is it?
X+1=2
Send us your name before 11PM.
I request you to please allow me a day off.
Fetch my umbrella!
Conjunction:
Let p and q be propositions. The conjunction of p and q,
denoted by p∧q, is the proposition “p and q”.
The conjunction p ∧ q is true when both p and q are true
and otherwise false.
Truth table for Conjunction :
p
T
T
F
F
q
T
F
T
F
p∧q
T
F
F
F
Disjunction:
Let p and q be propositions. The disjunction of p and q,
denoted by p ∨ q, is the proposition “p or q”.
The disjunction p ∨ q is false when both p and q are false ,
otherwise true.
Truth table for Disjunction :
p
q
T
T
F
T
F
T
p∨q
T
T
T
F
F
F
Implication :
Let p and q be propositions . The conditional statement
p → q, is the proposition “if p, then q”.
The conditional statement p → q is false when p is true and
q is false, otherwise true.
Truth table for Implication :
p
T
T
F
F
q
T
F
T
F
p→q
T
F
T
T
Bi-implication :
Let p and q be propositions.The biconditional statement
p↔q, is the proposition “p if and only if q”.
The bi-implication statement p↔q is true when p and q has
same truth values, otherwise false.
Truth tabler for bi-implication :
p
T
T
F
F
q
T
F
T
F
p ↔q
T
F
F
T
Converse :
Let p→q be a conditional statement then q→p is called
converse.
Truth tabler for Converse :
p
T
T
F
F
q
T
F
T
F
p→ q
T
F
F
T
q→p
T
T
F
T
Contrapositive :
Let p→q be a conditional statement then ¬q→¬p is called
contrapositive of that conditional statement.
Truth table for Contrapositive :
p
q
p→q
¬p
¬q
¬q→¬p
T
T
T
F
F
T
T
F
F
F
T
F
F
T
T
T
F
T
F
F
T
T
T
T
Inverse :
Let p→q be a conditional statement then ¬ p→¬ q is called its
inverse.
Truth table for Inverse:
p
q
p→q
¬p
¬q
¬p→¬q
T
T
T
F
F
T
T
F
F
F
T
T
F
T
T
T
F
F
F
F
T
T
T
T
THANK YOU