CONDITIONALS. Conditional Statement: Any statement that is or can be written in if- then form. That is, If p then q.

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Presentation transcript:

CONDITIONALS

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”:

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 CONDITIONALS

The Converse: The conditional statement formed by interchanging the hypothesis and conclusion.

Symbolically, for the conditional statement: The converse is:

EXAMPLE: Form the converse of: IfthenX=2X > 0.

EXAMPLE: Form the converse of: IfthenX=2X > 0. IfthenX > 0X=2.

The Inverse: The conditional statement formed by negating both the hypothesis and conclusion.

Symbolically, for the conditional statement: The inverse is:

EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

The Contrapositive: The conditional statement formed by interchanging and negating the hypothesis and conclusion.

Symbolically, for the conditional statement: The contrapositive is:

EXAMPLE: Form the contrapositive of: IfthenX=2X > 0. IfthenX=2X > 0.

Note: Any statement and its Contrapositive 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. ? CONVERSE

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.? CONVERSE

THE END !!