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.
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.