Deductive Reasoning What can you DD DEDUCE Deductive

Deductive Reasoning What can you D…D…. DEDUCE ?

Deductive Reasoning • The process of using logic to draw conclusions from given facts, definitions, and properties Inductive or Deductive In Mrs. Tucker’s math class, girls tend to sit in the front. Jennifer is a girl, so she will probably be in front. Mrs. Tucker has a rule that all girls must sit in the front. Jennifer is a girl. Jennifer will sit in the front.

Deductive Reasoning • In deductive reasoning, if the given facts are true and you apply the correct logic, then the conclusion must be true. Deductive Reasoning Law of Detachment Law of Syllogism

Law of Detachment If p q is a true statement and p is true, then q is true Example 1: Given: If two segments are congruent, then they have the same length. Conjecture: AB = XY Identify the hypothesis and conclusion in the given conditional

Law of Detachment If p q is a true statement and p is true, then q is true Example 2: Given: If you are tardy 3 times, you must go to detention. Shea is in detention. Conjecture: Shea was tardy at least 3 times. Identify the hypothesis and conclusion in the given conditional

Law of Detachment If p q is a true statement and p is true, then q is true Determine if the conjecture is valid by the law of detachment Given: If a student passes his classes, the student is eligible to play sports. Ramon passes his classes. Conjecture: Ramon is eligible to play sports. Identify the hypothesis and conclusion in the given conditional

Law of Syllogism If p q and q r are true statements, then p r is a true statement. Given: If the electric power is cut, then the refrigerator does not work. If the refrigerator does not work, then the food is spoiled. The electric power is cut. Conclusion: Identify the p, q, and r in the given conditional

Law of Syllogism If p q and q r are true statements, then p r is a true statement. Identify the p, q, and r in the given conditional Given: If an animal is a mammal then it has hair. If an animal is a dog, then it is a mammal. Conclusion:

Law of Syllogism If p q and q r are true statements, then p r is a true statement. Given: If the calculator is broken, then it is not working. If the calculator has no battery, then it is not working. What can We Conclude? Identify the p, q, and r in the given conditional

Deductive Reasoning • In deductive reasoning, if the given facts are true and you apply the correct logic, then the conclusion must be true. Deductive Reasoning Law of Detachment If p q is a true statement and p is true, then q is true Law of Syllogism If p q and q r are true statements, then p r is a true statement.