Homework Questions

Homework Questions

1.) Define deductive reasoning.

2.) Use the Law of Detachment and the Law of Syllogism to form a logical argument.

2.3 Apply Deductive Reasoning

2.3 Apply Deductive Reasoning

Remember that inductive reasoning was where we found a pattern in specific cases and then made a conjecture about the general case.

deductive reasoning - uses ____________________________________ to form a logical argument.

facts, definitions, accepted properties, and laws of logic

2.3 Apply Deductive Reasoning

Laws of Logic

 Law of Detachment - If the hypothesis of a true conditional statement is true, then the conclusion is also true.

 Law of Syllogism - If hypothesis p, then conclusion q.If hypothesis q, then conclusion r.

If hypothesis p, then conclusion r. If both true,

then this statement is true.

2.3 Apply Deductive Reasoning

Ex. 1 Use the Law of Detachment to make a valid conclusion in the true situation.

 (a) If two segments have the same length, then they are congruent. you know that BC = XY.

 (b) Mary goes to the movies every Friday and Saturday night. Today is Friday.

2.3 Apply Deductive Reasoning

Ex. 2 Describe the pattern in the numbers. Write the next number in the pattern.

 4, 3, 1, -2...

Subtract 1, subtract 2, subtract 3... ; -6Q A

2.3 Apply Deductive Reasoning

Ex. 3 If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.

 (a) If Rick takes chemistry this year, then Jesse will be Rick's lab partner. If Jesse is Rick's lab partner, then Rick will get an A in chemistry.

2.3 Apply Deductive Reasoning

Ex. 3 If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.

 (b) If x2 > 25, then x2 > 20. If x > 5, then x2 > 25.

2.3 Apply Deductive Reasoning

Ex. 3 If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.

 (c) If a polygon is regular, then all angles in the interior of the polygon are congruent. If a polygon is regular, then all of its sides are congruent.

2.3 Apply Deductive Reasoning

Ex. 4 Write the converse, inverse and contrapositive of the conditional statement. Determine which are true and which are false.

 If you play guitar, then you are a musician.

Converse:

Inverse:

Contrapositive:If you are a musician, then you play guitar.If you don't play guitar, then you aren't a musician.  If you aren't a musician, then you don't play guitar.

AQ

2.3 Apply Deductive Reasoning

Ex. 5 Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.

 (a) Each time I throw a ball up, it returns to the ground. So the next time I throw a ball up, it will return to the ground.

 (b) All reptiles are cold-blooded. Parrots are not cold-blooded. My pet parrot is not a reptile.

2.3 Apply Deductive Reasoning

Laws of Logic

 Law of Detachment - If the hypothesis of a true conditional statement is true, then the conclusion is also true.

 Law of Syllogism - If hypothesis p, then conclusion q.If hypothesis q, then conclusion r.

If hypothesis p, then conclusion r. If both true,

then this statement is true.

2.3 Apply Deductive Reasoning

Homework:

 pg. 117 #6,7,10,11,12,13,15