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Implications

Implications. All prairie dogs are rodents If an animal is a prairie dog, then it is a rodent. This IMPLIES that EVERY prairie dog is a rodent Hypothesis - If an animal is a prairie dog Conclusion - then it is a rodent An animal is a prairie dog only if it is a rodent. Implications.

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Implications

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  1. Implications All prairie dogs are rodents If an animal is a prairie dog, then it is a rodent. This IMPLIES that EVERY prairie dog is a rodent Hypothesis - If an animal is a prairie dog Conclusion - then it is a rodent An animal is a prairie dog only if it is a rodent

  2. Implications Hypothesis – the “if” part of a conditional statement Conclusion – the “then” part of a conditional statement Implication – a statement that cal be written in the form p -- q (Read “p implies q” or “If p, then q”) Conditional – a statement that can be written in the form p- q:

  3. Implications The New England states are east of the Mississippi River If a state is in New England, Then it is east of the Mississippi. Counterexample – Virginia is east of the Mississippi River, but it is not a New England state

  4. Implications This month is February if today is Valentines Day REWRITE THE IMPLICATION If today is Valentines Day Then it’s the month of February TRUE

  5. Implications This month is February if today is Valentines Day WRITE THE CONVERSE If it’s the month of February Then its Valentines Day FALSE COUNTEREXAMPLE It could be February 11th

  6. Implications Rectangles are parallelograms REWRITE THE IMPLICATION If the polygon is a rectangle Then it is a parallelogram TRUE

  7. Implications Rectangles are parallelograms WRITE THE CONVERSE If the polygon is a parallelogram Then it is a rectangle FALSE Counterexample It could be a Rhombus

  8. Implications A number ending in 0 implies that it is divisible by 2. REWRITE THE IMPLICATION If a number ends in 0 Then the number is divisible by 2 TRUE

  9. Implications A number ending in 0 implies that it is divisible by 2. WRITE THE CONVERSE If a number is divisible by 2 Then the number ends in 0 FALSE Counterexample: 24 is divisible by 2 but doesn’t end in 0

  10. Implications Cleo is a golden retriever only if Cleo is a dog REWRITE THE IMPLICATION If Cleo is a golden retriever Then Cleo is a dog TRUE

  11. Implications Cleo is a golden retriever only if Cleo is a dog REWRITE THE CONVERSE If Cleo is a dog Then Cleo is a golden retriever False, counterexample It could be a German shepard

  12. Implications A Chord is a segment whose endpoints are on a circle chord

  13. Implications A Chord is a segment whose endpoints are on a circle Is the diameter of a circle a chord? Write an implication about chords and diameters. WRITING Write the converse of your implication. Is it true? Explain

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