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Inductive and Deductive Reasoning. 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.
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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.
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.
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 90o 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.
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 the inverse, converse and contrapositive of the conditional statement: “If two angles form a linear pair, then they are supplementary.” Which statements are always true?
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.
