### 2.3 Deductive Reasoning - Belle Vernon Area School District

```2.3 Deductive Reasoning
Deductive means
“a systematic method of deriving conclusions”
2-3 Deductive Reasoning
 You will use symbolic notation to represent
logical statements.
 You will learn to form conclusions by
applying the laws of logic to the statements
Symbolic Notation
p represents the hypothesis
q represents the conclusion
~ represents negation
If p then q can be written as p →q
Inverse statement ~p → ~q
Bi-conditional statement p ↔ q
How would you represent each of the
following “symbolically?”
Conditional
pq
Converse
q p
Inverse
Contrapositive
p q
q
p
Deductive Reasoning
 Deductive reasoning uses facts, definitions,
and accepted properties in a logical order to
write a logical argument.
 Inductive reasoning uses previous examples
and patterns to make a conjecture.
Laws of Deductive Reasoning
 Law of Detachment: If p →q is a true conditional
statement and p is true, that is, the situation
described in the hypothesis occurs, then q is true,
that is, the conditional situation also occurs.
If it snows 10 feet, then there is no school. It
just snowed 10 feet, so I can conclude there is no
school.
Laws of Deductive Reasoning
 Law of Syllogism: If p →q and q →r are true
conditional statement, then p →r is true
p: John gets a C
q: John passes the test
r: John plays football
If John gets a C, then john plays football.
Write the Converse, Inverse, and
Contrapositive in symbolic notation.
 C. Statement: If it is Wednesday, then I am not
home.
pq
 Converse: If I am not at home, then it is
Wednesday.
q p
 Inverse: If it is not Wednesday, then I am home.
p q
 Contrapositive: If I am home, then it is not
Wednesday.
q
p
Write the Converse, Inverse, and
Contrapositive (include symbolic notation).
 If 3 measures 90, then 3 is not acute.
pq
 If 3 is not acute, then 3 measures 90.
q p
 If 3 does not measure 90, then 3 is acute.
p q
 If 3 is acute, then 3 does not measure 90.
q
p
```