write the two conditional statements that make up each biconditional. 6. points are collinear if and only if they lie on the same line. 7. you will pass your test if and only if you get at least a 60%. explain why each of the following is not an acceptable definition. 8. opposite rays have a common endpoint. 9. a rabbit is an animal that hops. if possible, use the law of detachment to draw a conclusion. if not possible, write not possible. 10. if it is friday or saturday, then mary goes to the movies. it is friday. 11. if the measure of an angle is 60°, then it is acute. ∠a is acute. use the law of syllogism to draw a conclusion. 12. if you play the clarinet, then you play a woodwind instrument. if you play a woodwind instrument, then you are a musician.

Question

Accepted Answer

# 6.
## Brief Explanations:
A biconditional statement "p if and only if q" can be written as two conditional statements: "if p then q" and "if q then p". Here p is "Points are collinear" and q is "they lie on the same line".
## Answer:
If points are collinear, then they lie on the same line.
If points lie on the same line, then they are collinear.

# 7.
## Brief Explanations:
For the biconditional "You will pass your test if and only if you get at least a 60%", p is "You will pass your test" and q is "you get at least a 60%".
## Answer:
If you will pass your test, then you get at least a 60%.
If you get at least a 60%, then you will pass your test.

# 8.
## Brief Explanations:
A good definition should be reversible. Just having a common endpoint is not enough to define opposite - rays. Two rays with a common endpoint are not necessarily opposite rays; they must also form a straight line.
## Answer:
This is not a good definition because two rays with a common endpoint are not always opposite rays. Opposite rays must also form a straight - line.

# 9.
## Brief Explanations:
The statement is not a good definition as there are other animals that hop (like kangaroos), and not all rabbits may always hop (due to injury etc.). A definition should be unique and cover all cases precisely.
## Answer:
This is not a good definition because there are other animals that hop, and not all rabbits may hop in all situations.

# 10.
## Brief Explanations:
The Law of Detachment states that if "if p then q" is true and p is true, then q is true. Here p is "it is Friday or Saturday" and q is "Mary goes to the movies", and since "it is Friday" (which makes "it is Friday or Saturday" true).
## Answer:
Mary goes to the movies.

# 11.
## Brief Explanations:
The Law of Detachment requires the "if - then" statement's hypothesis to be true to draw a conclusion. Here we only know that ∠A is acute (the conclusion of the "if - then" statement), not that the measure of the angle is 60°.
## Answer:
Not possible

# 12.
## Brief Explanations:
The Law of Syllogism states that if "if p then q" and "if q then r" are true, then "if p then r" is true. Here p is "you play the clarinet", q is "you play a wood - wind instrument", and r is "you are a musician".
## Answer:
If you play the clarinet, then you are a musician.

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QUESTION IMAGE

Question

Explanation:

6.

Answer:

7.