# Deductive Reasoning

How to determine whether the given reasoning is a deductive reasoning: definition, 3 examples, and their solutions.

## Definition

### Definition

Deductive reasoning is a reasoning
that starts from [given & known statements]
to get a [specific conclusion],

usually by using [logic].

## Example 1

### Solution

The first statement is a conditional statement.

p: It's raining.
q: He's staying home.

Assume that this statement is true.

The second statement is p.

Assume that this statement is also true.

The third statement is q.

If the top two statements are true,
then q is true.

p → q and p [given statements] are both true.

Then, by the law of detachment,
which is [logic],
q [specific statement] is true.

So these statements show
deductive reasoning.

So [deductive reasoning] is the answer.

## Example 2

### Solution

x + 2 = 3 [given statement] is true.

Writing -2 on both sides
doesn't change the equal sign:
x + 2 - 2 = 3 - 2.
This is [logic].

Then x = 1 is true. [specific statement]

Linear Equation: One Variable

So these equations show
deductive reasoning.

So [deductive reasoning] is the answer.

## Example 3

### Solution

The first two [given statements] are true:
he went there yesterday,
he goes there today.

Then it says
the last statement is true:
he will go there tomorrow.

These statements show a pattern,
yesterday → today → tomorrow:
not logic.

So the given statements
do not show deductive reasoning.
(They show inductive reasoning.)

So [not deductive reasoning] is the answer.