Patterns and Reasoning | Conditional Statements | Related Conditional Statements | Biconditional Statements | Deductive Reasoning |
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81 and 243
What are the next two terms in 3, 9, 27, ...?
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An angle measures 130
What is the hypothesis of the statement
"If an angle measures 130, then the angle is obtuse" |
False
What is the truth value of "If A = 140º, then A is acute"
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No. Not reversible, Dolphins, Turtles, Whales also swim.
Is this a good definition?
"A fish is an animal that swims" |
Rachel will pass the course.
What can you conclude from the statement
"If a students gets an A on the final exam, then the student will pass the course. Rachel got an A on her history final exam." |
1/10 and 1/100 or 0.1 and 0.01
What are the next two terms in 100, 10, 1, ...
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They share a vertex
What is the conclusion of the statement
"If two angles are vertical, then they share a vertex" |
If a is not acute (Add not)
What is the negation of "If A is acute"
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Yes. If an angle is a straight angle, then it measures 180º
Is the following statement reversible?
"If an angle measures 180º, then it is a straight angle" |
No conclusion.
What can you conclude from the statement
"If two angles are adjacent, then they share a common vertex. Angles 1 and 2 share a common vertex." |
1/16 and 1/32
What are the next two terms in 1/2, 1/4, 1/8, ...
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If an animal is a dolphin, then it is a mammal.
How can you write "Dolphins are mammals" as a conditional statement?
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If A is acute, then A = 14º (Switch order)
What is the converse of "If A = 14º, then A is acute"
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If and only if
What four words are in a biconditional statement?
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If a figure is a square, then it has four sides.
What can you conclude from the statement
"If a figure is a square, then the figure is a rectangle. If a figure is a rectangle, then it has four sides." |
January
What is a counterexample for the statement
"If the name of a month starts with the letter J, it is a summer month." |
False. Example: 6/3=2 and 6 is even.
Is this conditional true or false?
"If a number is divisible by 3, then it is odd" |
If A ≠ 14º, then A is not acute (Add not)
What is the inverse of "If A = 14º, then A is acute"
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The conditional and the converse
Which 2 related conditionals need to be true for a biconditional statement?
Conditional, Converse, Inverse, Contrapositive |
No conclusion.
What can you conclude from the statement
"If you do gymnastics, then you are flexible. If you do ballet, then you are flexible." |
Any negative number. Ex: -2 x 2 = -4, -4 < -2
What is a counterexample for the statement
"When you multiply a number by 2, the product is greater than the original number." |
True
Is this conditional true or false?
"If two angles form a linear pair, then they are supplementary" |
If A is not acute, then A ≠ 14 (Add not and switch order)
What is the contrapositive of "If A = 14º, then A is acute"
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A polygon has four sides if and only if it is a quadrilateral
Write the statement as a biconditional.
"If a polygon has four sides, then it is a quadrilateral." |
Law of Detachment and Law of Syllogism
What is the name of the laws used to make conclusions from statements? (Need 1 of the 2 answers)
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