CONDITIONAL STATEMENT ANALISYS WITH TRUTH TABLE

1. CONJUNCTION
DISJUNCTION
IMPLICATION
BI-IMPLICATION
CONVERSE & INVERSE
CONTRAPOSITIVE

2. CONJUNCTION
• A conjunction is a compound
statement formed by joining two
statements with the connector
AND. The conjunction "p and q"
is symbolized by P∧Q . A
conjunction is true when both of
its combined parts are true;
otherwise it is false.
.
2
• Let us make a truth table for P and Q, i.e. P ∧
Q.
P Q P∧Q
T T T
T F F
F T F
F F F
Example : P: The number x is odd. Q: The number x is prime.
Problem: Can we list all truth values for R ∧ S in a truth table? Why or why not?
If x = 3, then P is true, Q is true. The conjunction P ∧ Q is true.
If x = 9, then P is true, Q is false. The conjunction P ∧ Q is false.
If x = 2, then P is false, Q is true. The conjunction P ∧ Q is false.
If x = 6, then P is false, Q is false. The conjunction P ∧ Q is false.

3. DISJUNCTION
• A disjunction is a compound
statement formed by joining two
statements with the connector OR.
The disjunction "p or q" is
symbolized by pq. A disjunction is
false if and only if both statements
are false; otherwise it is true. The
truth values of pq are listed in the
truth table below.
Example - P: x is divisible by 2. Q: x is divisible by 3.
Problem : What are the truth values of P∨Q
If x = 6, then P is true, and Q is true. The disjunction P∨Q is
true.
If x = 8, then P is true, and Q is false. The disjunction P∨Q is
true.
If x = 15, then P is false, and Q is true. The disjunction P∨Q
is true.
If x = 11, then P is false, and Q is false. The disjunction P∨Q
is false.
.
3
• Let us make a truth table for P and Q, i.e. P ∨
Q.
P Q P∨Q
T T T
T F T
F T T
F F F

4. IMPLICATION
• An implication is the
compound statement of the
form “if p, then q.” It is
denoted
• p → q, which is read as “p
implies q.” It is false only when
p is true and q is false, and is
true in all other situations.
.
4
• Let us make a truth table for P and Q, i.e. P →
Q.
P Q P→Q
T T T
T F F
F T T
F F T

5. BI-IMPLICATION
• A bi-conditional statement,
sometimes referred to as a bi-
implication, may take one the
following forms: P if and only if Q.
P is necessary and sufficient for
Q. If P then Q,and conversely.
.
5
• Let us make a truth table for P and Q, i.e.
P↔Q.
P Q P↔Q
T T T
T F F
F T F
F F T

6. CONVERSE & INVERSE
• In logic and mathematics, the converse of a categorical or implicational statement is the
result of reversing its two constituent statements. For the implication P → Q, the
converse is Q → P.
• An inverse unction or an anti function is defined as a function, which can reverse into
another function. In simple words, if any function “f” takes P to Q then, the inverse of
“f” will take Q to P.
.
6
CONTRAPOSITIVE
Statement If pp , then qq .
Converse If qq , then pp .
Inverse
If not pp , then
not qq .
Contrapositiv
e
If not qq , then
not pp .
• the contrapositive statement by interchanging the
hypothesis and conclusion of the inverse of the same
conditional statement.

7. THANK
YOU
PUNAM PRIYA