“The proof is in the pudding.”
“Indubitably.”
Le pompt de pompt le solve de crime!"
Je solve le crime. Pompt de pompt pompt."
Deductive Reasoning
2-1 Classroom Ex. P 34.
2-1 Classroom Ex. P 34.
Underline the hypothesis and box the conclusion.
1.
If 2x – 1 = 5, then x = 3.
2.
If she’s smart, then I’m a genius.
3.
8y = 40 implies y = 5
2-1 Classroom Ex. P 34.
Underline the hypothesis and box the conclusion.
4.
1
RS = RT if S is the midpoint of
2
5.
1  2 if m 1 m  2
6.
RT .
1  2 only if m 1 m  2
“only if” and “if” are not the same.
7. Convert 5 and 6 into a biconditional.
5.
6.
1  2 if m 1 m  2
1  2 only if m 1 m  2
1  2 if only if m 1 m  2
Provide a counterexample to show that each
statement is false. You may use words or a
diagram.
If AB  BC, then B is the
midpoint of AC .
8.
B
A
C
C
B
9.
If a line lies in a vertical plane,
then the line is vertical.
E
D
Horizontal line
If a number is divisible by 4, A
then it is divisible by 6.
8
10.
F
8 is divisible by 4 but it is
not divisible by 6.
Provide a counterexample to show that each
statement is false. You may use words or a
diagram.
11.
If X2 = 49, then x = 7.
-7
X2 = 49 is a quadratic
equation and has two
solutions.
State the converse of each conditional. Then indicate
if the converse is true or false. If false, state the
counterexample.
12.
If today is Friday, then tomorrow is Saturday.
If tomorrow is Saturday, then today is Friday.
True
State the converse of each conditional. Then indicate
if the converse is true or false. If false, state the
counterexample.
13. If x > 0 , then x2 > 0.
If
x2
> 0, then x > 0.
False If x = - 5+
Then (- 5)2 > 0
14. If a number is divisible by 6,
then it is divisible by 3.
If a number is divisible by 3,
then it is divisible by 6.
False 9
9 is divisible by 3
But 9 is not divisible
by 6.
State the converse of each conditional. Then indicate
if the converse is true or false. If false, state the
counterexample.
15. If 6x = 18 , then x = 3.
If x = 3, then 6x = 18.
True
16. Give an example of a false conditional whose
converse is true.
False If x = - 5+
Cond: If x2 > 0, then x > 0.
Conv: If x > 0, then x2 > 0.
Then (- 5)2 > 0
True positive
numbers squared are
always positive.
C’est fini.
Good day and good luck.