Question

Methods of Proof and Logic, Posting in comments

Answer 1

2. Explain whether the following statement is a valid definition: “A 150° angle is an obtuse angle.” Use the converse, biconditional, and at least one Euler diagram to support your answer.
Answer:

Answer 2

3. Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deductive reasoning and describe how each can help you develop and prove theorems.

Answer 3

2: def. supplementary angles

Answer 4

4. Start with the following statement:
Vertical angles are congruent.
a. State the conditional and three other forms of the statement.
b. If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? Use at least one truth table and at least one property to support your reasoning

Answer 5

2:linear pair so supplementary
3:def. supplementary
4:substitution (simplify)
5:division
6:def. right angle
7:def. perpendicular

Answer 6

4. a.
If angles are vertical angles, then they are congruent.
If angles are congruent, then they are vertical angles.
If angles are not vertical angles, then they are not congruent.
If angles are not congruent, then they are not vertical angles.

Answer 7

4. b. The conditional statement and the contrapositive have the same truth value. The inverse and converse have the same truth value.

Answer 8

By truth value I mean that if one is true the other is true and if one is false the other is false.

Answer 9

bro you really smart

Answer 10

2. This isn't a valid definition. If it were the conditional statement and the biconditional would be true.
Biconditional: An angle is obtuse iff it is 150 degrees.

Answer 11

iff means if and only if

Answer 12

not really sure about the rest but I hope I helped a little!