Download Conditional Statements

Conditional Statements
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SOL: G.1a
SEC: 2.3
Conditional Statement
Definition: A conditional statement is a statement that
can be written in if-then form.
“If _____________, then ______________.”
“if p, then q”. Symbolic Notation p → q
Lesson 2-1 Conditional Statements
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Conditional Statement
Conditional Statements have two parts:
The hypothesis is the part of a conditional statement that
follows “if” (Usually denoted p.)
The hypothesis is the given information, or the condition.
The conclusion is the part of an if-then statement that follows
“then” (Usually denoted q.)
The conclusion is the result of the given information.
Lesson 2-1 Conditional Statements
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Example
Write the statement “ An angle of 40° is acute.”
Hypothesis – An angle of 40° Represented by : p
Conclusion – is Acute
Represented by : q
If – Then Statement – If an angle is 40°, then the
angle is acute.
Example
Identify the Hypothesis and Conclusion in the
following statements:
p
q
1. If a polynomial has six sides, then it is a hexagon.
H: A polygon has 6 sides C: it is a hexagon
2. Tamika will advance to the next level of play if
she completes the maze in her computer game.
H: Tamika Completes the maze in her computer
game.
C: She will advance to the next level of play.
Forms of Conditional Statements
Conditional Statements:
Formed By: Given Hypothesis and Conclusion.
Symbols: p → q
Examples: If two angles have the same measure
then they are congruent.
Forms of Conditional Statements
Converse:
Formed By: Exchanging Hypothesis and conclusion
of the conditional.
Symbols: q → p
Examples: If two angles are congruent then they
have the same measure.
Forms of Conditional Statements
Inverse:
Formed By: Negating both the Hypothesis and
conclusion of the conditional.
Symbols: ~p →~q
Examples: If two angles do not have the same
measure they are not congruent.
Forms of Conditional Statements
Contra - positive:
Formed By: Negating both the Hypothesis and
conclusion of the Converse statement.
Symbols: ~q →~p
Examples: If two angles are not congruent then
they do not have the same measure.
Logically Equivalent Statements - are statements with the
same truth values.
Example: Write the converse, inverse and contra positive of the following statement:
Conditional: If a shape is a square, then it is a rectangle.
Converse: If a shape is a rectangle, then it is a square.
Inverse: If a shape is not a square, then it is not a
rectangle.
Contra-positive: If a shape is not a rectangle, then it is
not a square.
Try This:
Example: Write the converse, inverse and
contra - positive of the following statement:
Conditional: If two angles form a linear pair,
then they are supplementary.
Converse:
Inverse:
Contra – positive:
Assignments
Classwork: WB: pg 39 - 40 all
Homework: pg 93-95 6-24 even, 28, 32-34, 4345