1. } { Using facts, definitions, accepted properties and the
laws of logic to form a logical argument.
You can use the Law of Syllogism when the conclusion of one statement matches the hypothesis of the other.
conclusion { p q,
p implies q,
q implies r,
therefore, p implies r. }
Math/
Logic q r,
English
∴ p r

2. ∠A ≅ ∠B
it is a
weekday
Jesse goes to
the gym
Jesse will go to the gym today

3. he will drink a glass of milk
x2 > 30
hypothesis
LoD - uses a true conditional statement
followed by a second statement. If the
two things go together, we can draw a
conclusion without making an assumption.
LoS - if the conclusion of one if-then and conclusion
of another match, we can form a new if-then that
combines them.

4. ∠A is an acute angle.
The law of logic that's illustrated is the Law of Syllogism because the conclusion of one statement is the hypothesis of the other.

5. 2 4 8 -8 -4 -2
Even
even
Fact {
2n and 2m are Even 1
odd
even
Property of Addition {
2n - 1 and 2m +1 are Odd 1
odd
Sum of Odd Numbers {
(2n - 1) + (2m + 1) 1 2
Combine Like Terms and Factor {
2n + 2m
2(n + m) 2
even
It doesn't matter what number you get when you add n + m, if you multiply it by 2 you'll get an even number.

6. Test: = -2
= -12
= -10
-n + -n = -2n
The sum of a negative integer
and itself is twice the value
of the integer

7. Inductive
Deductive

8. Sample answer: The faster the average speed of
the runner, the less time he or she is running.
Sample answer: The runner's average speed is
faster when running for 10 minutes than when
running for 40 minutes.