Question

homework 2 - 5
teacher:
geometry
hour:
write the negation of each statement.

1. the soccer game is on friday.
2. the angles are not congruent.
3. m∠a = 90

use the symbolic notation to write the negation.

1. write ¬p: p: it is raining outside
2. write ¬p: p: the figure is a circle
3. write ¬p: p: (overline{xy}congoverline{yz})

write the inverse of each conditional statement.

1. if it is 12:00am, then it is midnight.
2. if an angle is obtuse, then the angle measures between 90 and 180 degrees.
3. if a number is a perfect square, then the square root is a whole number.
4. if you are 16 years or older, then you are legally allowed to drive.

Explanation:

Step1: Negate the statement

The negation of "The soccer game is on Friday" is "The soccer game is not on Friday".

Step2: Negate the statement

The negation of "The angles are not congruent" is "The angles are congruent".

Step3: Negate the statement

The negation of "m∠A = 90" is "m∠A≠90".

Step4: Use symbolic notation

If p: it is raining outside, then ¬p: it is not raining outside.

Step5: Use symbolic notation

If p: the figure is a circle, then ¬p: the figure is not a circle.

Step6: Use symbolic notation

If p: $\overline{XY}\cong\overline{YZ}$, then ¬p: $\overline{XY}
ot\cong\overline{YZ}$.

Step7: Find the inverse of the conditional

The inverse of "If it is 12:00am, then it is midnight" is "If it is not 12:00am, then it is not midnight".

Step8: Find the inverse of the conditional

The inverse of "If an angle is obtuse, then the angle measures between 90 and 180 degrees" is "If an angle is not obtuse, then the angle does not measure between 90 and 180 degrees".

Step9: Find the inverse of the conditional

The inverse of "If a number is a perfect square, then the square - root is a whole number" is "If a number is not a perfect square, then the square - root is not a whole number".

Step10: Find the inverse of the conditional

The inverse of "If you are 16 years or older, then you are legally allowed to drive" is "If you are not 16 years or older, then you are not legally allowed to drive".

Answer:

1. The soccer game is not on Friday.
2. The angles are congruent.
3. m∠A≠90
4. it is not raining outside
5. the figure is not a circle
6. $\overline{XY}

ot\cong\overline{YZ}$

1. If it is not 12:00am, then it is not midnight.
2. If an angle is not obtuse, then the angle does not measure between 90 and 180 degrees.
3. If a number is not a perfect square, then the square - root is not a whole number.
4. If you are not 16 years or older, then you are not legally allowed to drive.