Conditionals and Deductive Reasoning

Multiple Choice

Error Analysis: Jess is writing the converse statement of the following conditional statement: "If it is cold, then I will wear a jacket." She writes: "If it isn't cold, then I won't wear a jacket." Is she correct? If not select the type of statement she created.

• She is correct. Converse

• Contrapositive

• Inverse

• Contraverse

Unit 1 L6
Deductive Reasoning

Law: "if p, then q" is true, and "p" is true, then "q" must also be true.

​Law of Detachment

Process that involves drawing specific conclusions from general premises.

​Deductive Reasoning

Concepts:

(1) If p , then q .
(2) If q , then r .
Then we can derive:
(3) If p , then r .

​Example:

A pattern used in mathematical logic to help make logical decisions.

​Law of Syllogism

Concept:

1) Based on facts.
2) General ------>Specific
3) Conclusive

Deductive

1) Uses patterns to make  generalizations, rules.
2) Specific---->General
3) Scientific

​Inductive

Inductive Vs. Deductive

Example 1:

Inductive or Deductive:

If I draw 3 cards from a deck, then the three cards that are drawn are 2, 5, 11. Ben thinks the rule is every other prime number is drawn.

Example 2:

Inductive or Deductive:

If I know Benadryl helps me sleep, then I take two Benadryl. I will sleep.