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Mathematical Reasoning and Logical Statements

Mathematical Reasoning and Logical Statements. How to Speak Math… (In a Strange Way). VOCABULARY : INDUCTIVE REASONING DEDUCTIVE REASONING CONDITIONAL STATEMENT HYPOTHESIS CONCLUSION CONVERSE INVERSE NEGATION CONTRAPOSITIVE BICONDITIONAL.

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Mathematical Reasoning and Logical Statements

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  1. Mathematical ReasoningandLogical Statements How to Speak Math… (In a Strange Way)

  2. VOCABULARY : • INDUCTIVE REASONING • DEDUCTIVE REASONING • CONDITIONAL STATEMENT • HYPOTHESIS • CONCLUSION • CONVERSE • INVERSE • NEGATION • CONTRAPOSITIVE • BICONDITIONAL

  3. Inductive Reasoning – reasoning that involves using specific examples to make a conclusion. Deductive Reasoning – reasoning that involves using a general rule to make a conclusion. Examples: Inductive Reasoning…Jason sees a line of 10 school buses, and he notices that each one is yellow. He concludes that all school buses are yellow. Deductive Reasoning…Eva has been told that every taxi in New York City is yellow. When she sees a red car in NYC, she concludes that it is not a taxi.

  4. CONDITIONAL STATEMENTS Consider the statement: If a parallelogram has 4 right angles, then it is a rectangle. The statement above is called a conditional statement. It consists of a hypothesis and a conclusion. Conditional statements are often written it the form “If, then.” For the rectangle statement above, The Hypothesis(p)would be a parallelogram has 4 right angles The Conclusion (q)would be it is a rectangle. Logical Notation: p q Read as “p implies q”

  5. Manipulating Conditional Statements Negation– Changing the form of a statement by adding the word “not”. Converse – Reversing the order of a conditional statement. q p “q implies p” Inverse– Negating both the hypothesis and conclusion of a conditional statement. ~ p ~ q “not p implies not q” Contrapositive- The inverse of the converse. ~ q ~ p “not q implies not p” Biconditional Statement – A statement written in the form “If and only if”. Both the conditional and its converse must be true. p q

  6. Consider again the statement: If a parallelogram has 4 right angles, then it is a rectangle. Identify the Hypothesis. Identify the Conclusion. State the Negation. State the Converse. State the Inverse. State the Contrapositive.

  7. If a parallelogram has 4 right angles, then it is a rectangle. Identify the Hypothesis. If a parallelogram has 4 right angles Identify the Conclusion. it is a rectangle State the Negation. If a parallelogram has 4 right angles, then it is not a rectangle. State the Converse. If a parallelogram has is a rectangle, then it has 4 right angles. State the Inverse. If a parallelogram does not have 4 right angles, then it is not a rectangle. State the Contrapositive. If a parallelogram has is not a rectangle, then it does not 4 right angles. Biconditional: A parallelogram has 4 right angles if and only if it is a rectangle.

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