Page 181 - Math Course 2 (Book 2)
P. 181
Conditional Statements
If two angles do not have the same
Inverse negating both the hypothesis and ~p → ~q measure, then they are not
conclusion of the conditional
congruent.
negating both the hypothesis and If two angle are not congruent, then
Contrapositive conclusion of the converse ~q → ~p they do not have the same
statement measure.
Let’s Begin
Truth Values of Conditionals Related Conditionals
Examples Example
Determine the truth value of the following Write the converse, inverse, and contrapositive of
statement for each set of conditions. If Yukon the statement All squares are rectangles.
rests for 10 days, his ankle will heal.
Determine whether each statement is true or false.
The hypothesis is true, but the conclusion is false. If a statement is false, give a counterexample.
First, write the conditional in if-then form.
Since the result is not what was
Answer expected, the conditional Conditional If a shape is a square, then it is a
statement is false. rectangle.
The conditional statement is true
The hypothesis is false, and the conclusion is
false. The statement does not say what happens
if Yukon only rests for 3 days. His ankle could Write the converse by switching the hypothesis
possibly still heal.
and conclusion of the conditional.
In this case, we cannot say that Converse If a shape is a rectangle, then it is a
Answer the statement is false. Thus, the square.
statement is true. The converse is false.
The hypothesis is true since Yukon rested for 10 Counterexample: A rectangle with = 2 and w = 4
days, and the conclusion is true because he does is not a square.
not have a hurt ankle.
Inverse If a shape is not a square, then it is not
a rectangle.
Since what was stated is true,
Answer The inverse is false.
the conditional statement is true.
Counterexample: A 4-sided polygon with side
The hypothesis is false, and the conclusion is lengths 2, 2 , 4 and 4 is not a square.
true. The statement does not say what happens if
Yukon only rests for 7 days. The contrapositive is formed by negating the hy-
pothesis and conclustion of the converse.
In this case, we cannot say that Contrapositive If a shape is not a rectangle,
Answer the statement is false. Thus, the then it is not a square.
statement is true. The contrapositive is true.
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