Inductive and Deductive Reasoning. Notecard 29 Definition: Conjecture: an unproven statement that is based on observations. You use inductive reasoning.

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Presentation transcript:

Inductive and Deductive Reasoning

Notecard 29 Definition: Conjecture: an unproven statement that is based on observations. You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case.

Write a conjecture Look at the patterns below and write a conjecture for the next number in the sequence ? ?

Notecard 30 Definition: Counterexample: a specific case for which a conjecture is false.

Counterexample Find a counter example to show that the following conjecture is false. The sum of two numbers is always greater than the larger number.

Notecard 31 Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is logical statement that has two parts: The hypothesis is the “if” part of the conditional statement. The conclusion is the “then” part of the conditional statement.

Writing a conditional statement: The hypothesis tells you what you are talking about, and the conclusion describes the hypothesis.

Writing a conditional statement Writing the following statements in if-then form. Two angles that make a linear pair are supplementary. All 90 o angles are right angles.

Vocabulary The negation of a statement is the opposite of the original.

Negation Negate the following statements. The ball is red. The cat is not black.

Notecard 32 Definitions: Inverse, Converse, Contrapositive The inverse of a conditional statement negates the hypothesis and conclusion The converse of a conditional statement switches the hypothesis and conclusion. The contrapositive of a conditional statement takes the inverse of the converse.

Writing statements Write he inverse, converse and contrapositive of the conditional statement: “If two angles form a linear pair, then they are supplementary.” Which statements are always true?

Notecard 33 Definition: Biconditional: If a conditional statement and its converse are both true, then we can write it as a biconditional statement by using the phrase if and only if instead of putting it in if-then form.

Biconditional Statement Write the following conditional statement as a biconditional statement. If two lines intersect to form a right angle, then they are perpendicular.