lecture conditional statements .ppt

conditional statements

1. Lesson 2-1 Conditional
Statements
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Lesson 2-1
Conditional
Statements

2. Lesson 2-1 Conditional
Statements
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Conditional Statement
Definition:A conditional statement is a statement that
can be written in if-then form.
“If _____________, then ______________.”
Example:Ifyour feet smell and your nose runs, then
you're built upside down.
Continued……

3. Lesson 2-1 Conditional
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Conditional Statement -continued
Conditional Statements have two parts:
The hypothesisis the part of a conditional statement that follows
“if”(when written in if-then form.)
The conclusionis the part of an if-then statement that follows
“then”(when written in if-then form.)
The hypothesis is the given information, or the condition.
The conclusion is the result of the given information.

4. Lesson 2-1 Conditional
Statements
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Conditional statements can be written in “if-then”form to
emphasize which part is the hypothesis and which is the
conclusion.
Writing Conditional Statements
Hint: Turn the subject into the hypothesis.
Example 1:Vertical angles are congruent.can be written as...
Iftwo angles are vertical, thenthey are congruent.
Conditional
Statement:
Example 2:Seals swim. can be written as...
Conditional
Statement:Ifan animal is a seal, thenit swims.

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If …Thenvs. Implies
Two angles are verticalimplies they are congruent.
Another way of writing an if-then statement is using
the word implies.
Iftwo angles are vertical, thenthey are congruent.

6. Lesson 2-1 Conditional
Statements
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Conditional Statements can be true or false:
A conditional statement is false only whenthe hypothesis is true,
but the conclusion is false.
A counterexampleis an example used to show that a
statement is not always true and therefore false.
If you live in Virginia, then you live in Richmond.Statement:
Counterexample:I live in Virginia, BUTI live in Glen Allen.
Is there a counterexample?
Therefore()the statement is false.
Yes !!!

7. Lesson 2-1 Conditional
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Symbolic Logic
Symbols can be used to modify or connect statements.
Symbols for Hypothesis and Conclusion:
Hypothesisis represented by “p”.
Conclusionis represented by “q”.
if p, then q
or
pimplies q
Continued…..

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Symbolic Logic -continued
if p, then q
or
p implies q
is used to representp q
Example:
p: a number is prime
q: a number has exactly two divisors
If a number is prime,then it has exactly two divisors.pq:
Continued…..

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is used to represent the word“not”~
Symbolic Logic -continued
Example 1:p: the angle is obtuse
The angle is not obtuse
~p means that the angle could be acute, right, or straight.
~p:
Note:
Example 2:p: I am not happy
~p: I am happy
~p took the “not” out-it would have been a double negative (not not)

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is used to represent the word
Symbolic Logic -continued
“and”
Example:
p:a number is even
q: a number is divisible by 3
A number is even and it is divisible by 3.
i.e. 6,12,18,24,30,36,42...
pq:

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is used to represent the word
Symbolic Logic-continued
“or”
Example:
p: a number is even
q: a number is divisible by 3
pq: A number is even or it is divisible by 3.
i.e.2,3,4,6,8,9,10,12,14,15,...

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is used to represent the word“therefore”
Symbolic Logic -continued

Example:Therefore, the statement is false.
the statement is false

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Forms of Conditional Statements
Converse:Switch the hypothesis and conclusion (q p)
pqIftwo angles are vertical, thenthey are congruent.
qpIftwo angles are congruent, thenthey are vertical.
Continued…..

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Forms of Conditional Statements
Inverse:State the opposite of both the hypothesis and conclusion.
(~p~q)
pq :Iftwo angles are vertical, thenthey are congruent.
~p~q:Iftwo angles are notvertical, thenthey are not
congruent.

15. Lesson 2-1 Conditional
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Forms of Conditional Statements
Contrapositive: Switch the hypothesis and conclusion and
state their opposites. (~q~p)
pq: Iftwo angles are vertical, thenthey are congruent.
~q~p:Iftwo angles are notcongruent, thenthey are not
vertical.

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Forms of Conditional Statements
Contrapositives are logically equivalent to the
original conditional statement.
If pq is true, then qp is true.
If pq is false, then qp is false.

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Biconditional
When a conditional statement and its converse are both true,
the two statements may be combined.
Use the phrase if and only if(sometimes abbreviated: iff)
Statement:If an angle is right then it has a measure of 90.
Converse:If an angle measures 90, then it is a right angle.
Biconditional:An angle is right if and only if it measures 90.