conditionals. conditional statement: any statement that is or can be written in if- then form. that...

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 !!