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