conditionals. conditional statement: any statement that is or can be written in if- then form. that...
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CONDITIONCONDITIONALSALS
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Conditional Statement:
Any statement that is or can be written in if-then form. That is,
If p then q.
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Symbolically we use the following for the conditional statement: “If p then q”:p q
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Hypothesis: The “condition” that has to be met. It is the p statement that follows the word if in a conditional statement.
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Conclusion: The result or consequence. The q statement that follows the then in a conditional statement.
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EXAMPLE:
If you feed the dog, then you may go to the movies.
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EXAMPLE:
If you feed the dog, then you may go to the movies.
Hypothesis
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EXAMPLE:
If you feed the dog, then you may go to the movies.
Hypothesis
Conclusion
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EXAMPLE:
The game will be cancelled if it rains.
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EXAMPLE:
The game will be cancelled if it rains.
Hypothesis
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EXAMPLE:
The game will be cancelled if it rains.
Hypothesis
Conclusion
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Note: The hypothesis does not always appear first in a statement.
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“ALL” Statements:When changing an “all” statement to if-then form, the hypothesis must be made singular.
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EXAMPLE: All rectangles have four sides.BECOMES: If _______ a rectangle then _____ four sides.
a figure is it
has
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RELATED RELATED CONDITIONCONDITIONALSALS
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The Converse:The conditional
statement formed by interchanging the hypothesis and conclusion.
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Symbolically, for the conditional statement:p qThe converse is:
q p
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EXAMPLE: Form the converse of:
If then
X=2
X > 0
.
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EXAMPLE: Form the converse of:
If then
X=2
X > 0
.If then
X > 0
X=2
.
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The Inverse:The conditional statement formed by negating both the hypothesis and conclusion.
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Symbolically, for the conditional statement:p qThe inverse is:
p q
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EXAMPLE: Form the Inverse of:
If then
X=2
X > 0
.If then
X=2
X > 0
.
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EXAMPLE: Form the Inverse of:
If then
X=2
X > 0
.If then
X=2
X > 0
.
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The Contrapositive:The conditional statement formed by interchanging and negating the hypothesis and conclusion.
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Symbolically, for the conditional statement:p qThe contrapositive is: q p
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EXAMPLE: Form the contrapositive of:If the
nX=2
X > 0
.If then
X=2
X > 0
.
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Note: Any statement and itsContrapositive have the same truth value.
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LET’S PRACTICE !
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GIVEN: If x is 5 then x is odd.
What form is: If x is odd then x is 5. ?CONVER
SE
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GIVEN: If x is 5 then x is odd.
What form is: If x is not odd then x is not 5. ?CONTRAPOSITIVE
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GIVEN: If x is 5 then x is odd.
What form is: If x is not 5 then x is not odd. ?INVERSE
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GIVEN: If x is odd then x is 5. What form is:
If x is 5 then x is odd.?CONVER
SE
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THE END !!