2. Conditional
statements and
material
implication
Presented by: Majid khan
Roll no : 13
BBA morning

3. Conditional statement
when two statements are combined by
placing the word “if” before the first
statement and “then” before the second
statement is called conditional statement
 eg. If Mr. A work hard then he will pass.

4. Conditional statement
 We use the arrow → or horseshoe to
represent the “if-then” phrase
 Also called a hypothetical statement

5. Components of conditional
statement
There are two components of conditional
statement
o The component statement that follows
the “if” is called the antecedent
o The component statement that follows
the “then” is called the consequent
o If (antecedent), then (consequent)

6. Conditional Statement
A conditional statement does not assert
that the antecedent is necessarily true. It
only asserts that if the antecedent is
true, then the consequent is true. And a
conditional statement does not assert
that the consequent is necessarily true. It
asserts that the consequent is true only if
the antecedent is true.

7. Material
Implication

8. Material implication
A conditional statement describes a
relationship between the antecedent and
the consequent. This relationship is called
"material implication"
Denoted by: “=>” or

9. For Example
 If you study hard, then you will pass.
Antecedent Consequent
=>
If p, then q.

10. Material implication
Then the relationship of material implication
between p and q is symbolized as p => q+
and is read “p implies q”.

11. Truth Table
p Q P => q
T T T
T F F
F T T
F F T
“p => q” is false if antecedent p is true
and consequent q is false; otherwise,
true.

12. Logical Implication
 The consequent follows logically from its
antecedent
 If
all humans are mortal and Socrates is a
human, then Socrates is mortal.

13. Definitional Implication
 The consequent follows the antecedent
by definition
 If
Leslie is a bachelor, then Leslie is
unmarried.

14. Causal Implication
 Theconnection between antecedent
and consequent is discovered empirically
 If I put X in acid, then X will turn red.

15. Decisional Implication
 No logical connection nor one by
definition between the consequent and
antecedent. This is a decision of the
speaker to behave in the specified way
under the specified circumstances.
 Is we lose the game, then I’ll eat my hat.

16. Thank you