Section 2.1 Notes
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Transcript of Section 2.1 Notes
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Section 2.1 Notes
Conditional Statements
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Conditional Statement
A type of logic statement that has two parts:
a hypothesis and a conclusion
We will write the conditional statements in If-Then Form. When written in this form the if part is the _____________ and the then part is the ____________.conclusion
hypothesis
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Example 1: Write in If-Then form and state the hypothesis and conclusion
1) Two points are collinear if they lie on the same line.
If-Then Form:
Hypothesis:______________________
Conclusion:_________________
If two points lie on the same line, then they are collinear.
Two points lie on the same line
they are collinear
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Example 2: Write in If-Then form and state the hypothesis and conclusion
2) All mammals breathe oxygen.
If-Then Form:
Hypothesis:_______________
Conclusion:_______________
If an animal is a mammal, then it breathes oxygen.
an animal is a mammal
it breathes oxygen
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More Logic Definitions The negative of a statement is the _________. Its
symbol is the ~. (tilda)
____________ is a statement formed by switching the hypothesis and the conclusion of a conditional statement.
________ is a statement formed by negating the hypothesis and the conclusion of a conditional statement.
_____________ is a statement formed by negating the hypothesis and the conclusion of the converse of a conditional statement.
negation
Converse
Inverse
Contrapositive
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Example 3: Write each statement and decide T or F
1) Conditional Statement:
If m<A = 30°, the <A is acute.
Converse: _____________________________
Inverse:_______________________________
Contrapositive:_________________________
If <A is acute, then the m<A = 30 º False, because an acute angle can be from 0 to 89.9
If m<A ≠ 30 º, then <A is not acute
False, could be a 20o angle
If <A is not acute, then m<A≠ 30 º
True
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2) Conditional Statement:
If an animal is a fish, then it can swim.
Converse: _____________________________
Inverse:_______________________________
Contrapositive:_________________________
If an animal can swim, then it is a fish
False; other animals can swim (turtle)
False; other animals can swim (turtle)
True
If an animal is not a fish, then it can’t swim
If an animal can’t swim, then it is not a fish
Example 4: Write each statement and decide T or F
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When two statements are both true or both false, they are called
In the ex 3 and 4, which statements are equivalent?
equivalent statements
Example 1:
Example 2:
Contrapositive and C.S.Converse and Inverse
C.S. and ContrapositiveConverse and Inverse
This will always be the case
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Point, Line, and Plane Postulates
Postulate 5: Through any two points there exists exactly _______________.
Postulate 6: A _______ contains at least two points.
Postulate 7: If two lines intersect, then their intersection is exactly ___________.
Postulate 8: Through any three noncollinear points there exists exactly ______________.
one line
line
one point
one plane
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Postulates ctd.
Postulate 9: A _________ contain at least three noncollinear points.
Postulate 10: If two points lie in a plane, then the line containing them lies in the _________.
Postulate 11: If two planes intersect, then their intersection is a __________.
plane
plane
a line