Which biconditional is not a good definition?
A whole number is odd if and only if the number is not divisible by 2.
An angle is straight if and only if its measure is 180°.
A whole number is even if and only if it is divisible by 2.
A ray is a bisector of an angle if and only if it splits the angle into two angles.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
I can go to the concert if I can afford to buy a ticket.
I can go to the concert.
a. I can afford to buy a ticket.
b. I cannot afford to buy ticket.
c. If I can go to the concert, I can affort the ticket.
d. not possible.

Question

08-08-2016
Mathematics

contestada

Which biconditional is not a good definition?
A whole number is odd if and only if the number is not divisible by 2.
An angle is straight if and only if its measure is 180°.
A whole number is even if and only if it is divisible by 2.
A ray is a bisector of an angle if and only if it splits the angle into two angles.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
I can go to the concert if I can afford to buy a ticket.
I can go to the concert.
a. I can afford to buy a ticket.
b. I cannot afford to buy ticket.
c. If I can go to the concert, I can affort the ticket.
d. not possible.

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MsEHolt MsEHolt · Answer 1 · 2018-06-25T03:43:54+02:00

The correct answers are:

A ray is a bisector of an angle if and only if it splits the angle into two angles; and
A) I can afford to buy a ticket.

Explanation:

For the first question, the first three answers are very specific and true:

A whole number is odd if it is not divisible by 2, and a number is not divisible by 2 if it is odd;
an angle is straight if its measure is 180 degrees, and the measure of an angle is 180 degrees if it is a straight angle;
a whole number is even if it is divisible by 2, and a number is divisible by 2 if it is even.

However, with the fourth choice, we are missing a key word in the definition. A ray is a bisector of an angle if and only if it splits the angle into two CONGRUENT angles. It is not just a ray that cuts an angle into two pieces, the pieces must be equal.

For the second question, the Law of Detachment says if our conditional "if p, then q" is true and p is true, then q must also be true.

For this question, "I can go to the concert if I can afford to buy a ticket" is true as well as "I can go to the concert." This means "I can afford to buy a ticket" must be true as well.