2-2 Conditional Statements
Conditional Statement—is a statement that can be written in the form of “if p, then q.”
In symbol, it is p  q
Hypothesis—the “p” part of a conditional statement. It the part of the statement following the
word “if.”
Conclusion—the “q” part of a conditional statement. It is the part of the statement following
the word “then.”
If two lines interest, then they intersect in exactly one point.
I’ll buy the book, if I have enough money.
Writing a statement as a conditional statement. To do this, decide which part of statement
depends upon the other.
EX: Cars with underinflated tires waste gasoline.
If a car has underinflated tires, then it wastes gasoline.
Ex: An obtuse triangle has exactly one obtuse angle.
If a triangle is obtuse, then it has exactly one obtuse angle.
Counterexample-- An example that proves that a conjecture or statement is false. You only
need one counterexample to prove the statement is false.
If the sidewalk is false, then it is raining. False—could be a sprinkler, snowing, etc
Negation—is the opposite. “p” becomes “not p” or ~p .
Converse—The converse the conditional statement interchanges (switches) the hypothesis and
the conclusion. “If p, then q” now becomes “If q, then p”
Example:
Statement:
If I get a date, then I will go to the Homecoming Dance.
Converse:
If I go to the Homecoming Dance, then I have a date.
Statement: If I am eating lima beans, I am eating a green vegetable.
Converse: If I am eating a green vegetable, then I am eating lima beans.
Statement: If I play high school soccer in Ohio, then I play in the fall season.
Converse: If I play in the fall, then I play high school soccer.
Statement: If a quadrilateral is a rhombus, then it has a pair of parallel sides.
Converse: If a quadrilateral has a pair of parallel sides, then it is a rhombus.
Statement: If two lines are parallel, then they do not intersect.
Converse: If two lines do not intersect, then they are parallel.
Remember: Do not assume that the converse of statement or theorem is true just because
the original statement is true. The converse of a theorem must be proved true!!
Conditional Statement—“If p, then q” p  q
Inverse—“If NOT p, then NOT q.” ~ p  ~q
Converse—Íf q, then p.
qp
Contrapositive—“If NOT q, then NOT p” ~ q  ~ p
Statement: A square is a rhombus
Conditional—If a quadrilateral is a square, then it is a rhombus.
True
Inverse—If a quadrilateral is not a square, then it is not a rhombus.
False
Converse—If a quadrilateral is a rhombus, then it is a square.
False
Contrapositive—If a quadrilateral is not a rhombus, then it is not a square.
True
Statement: An equilateral triangle is an isosceles triangle
Conditional: If a triangle is equilateral, then it is isosceles.
True
Inverse: If a triangle is not equilateral, then it is not isosceles.
False
Converse: If a triangle is isosceles, then it is equilateral.
False
Contrapositive: If a triangle is not isosceles, then it is not equilateral.
True
Writing a conditional statement from a Venn Diagram. The inner oval represents the
hypothesis and the outer oval represents the conclusion.
If an animal is a blue jay, then it is
a bird.
Birds
Blue Jay