B. Use Law of Detachment to draw conclusion
1. If two lines are parallel, then they do not intersect.
Lines j and k are parallel.
2. If there is lightning, then it is not safe to play outside.
Peter saw lightning.
3. If you get an average grade of 95– 100, then you will be in the honor roll
Your average grade is 95.25.
4. If a figure is a triangle, then the sum of the angles is 1800.
PQR is is a triangle.
5. If the sum of two angles is equal to 90 degrees, then the angles are com
plementary.
Angle x is equal to 30 degrees and angle y is equal to 60 degrees.
6. If two circles have the same center, then they are concentric.
The center of two circles is point A.
7. If a figure has 4 sides, then it is a quadrilateral
Square has 4 sides.
8. If the 2 integers are odd, then the sum is even number
The numbers x and y are odd integers.
9. If the score in math exam is 50 and above, then you passed the exam.
Rick scored 68 in the exam.
10. If points lie on a line, then they are collinear.
Points X, Y, and Z are in line m.
C. Use Law of Syllogism to draw conclusion. Determine if your conclusion is
valid or not. Justify your answer
1. If it continue to rain then, then the track and field oval will become wet and
slippery.
If the track and field oval will become wet and slippery, then the track and
field game will be cancelled.
2. If you are resting, then you will be relaxed.
If you are relaxed, then your heart beat is normal.
3. If you study your lesson, then you will pass the exam.
If you pass the exam, you will get a good grade.
4. If it creature is a fly , then it has and antennae.
If the creature has antennae, then it is an insect.
5. If you are studying science, then you are studying biology.
If you are studying biology, then you are studying botany.
6. If two lines are parallel, then they belong to one plane.
If lines belong to one plane, then they are coplanar.
7. If angles are linear pair, then they are supplementary angles.
If the angles are supplementary, the sum of the angles is 1800.
8. If a man is good in Math, then he is an engineer.
If he is an engineer, then he can build a house.
9. If a creature is a mammal, then it has 2 legs.
If a creature has 2 legs, then it can swim
10. If it rain, then there is lightning
If there is lightning, then there is thunder.
*I-I need help HUHU*
non-sense answers; auto report
1. If two lines are parallel, then they do not intersect.
Lines j and k are parallel.
2. If there is lightning, then it is not safe to play outside.
Peter saw lightning.
3. If you get an average grade of 95– 100, then you will be in the honor roll
Your average grade is 95.25.
4. If a figure is a triangle, then the sum of the angles is 1800.
PQR is is a triangle.
5. If the sum of two angles is equal to 90 degrees, then the angles are com
plementary.
Angle x is equal to 30 degrees and angle y is equal to 60 degrees.
6. If two circles have the same center, then they are concentric.
The center of two circles is point A.
7. If a figure has 4 sides, then it is a quadrilateral
Square has 4 sides.
8. If the 2 integers are odd, then the sum is even number
The numbers x and y are odd integers.
9. If the score in math exam is 50 and above, then you passed the exam.
Rick scored 68 in the exam.
10. If points lie on a line, then they are collinear.
Points X, Y, and Z are in line m.
C. Use Law of Syllogism to draw conclusion. Determine if your conclusion is
valid or not. Justify your answer
1. If it continue to rain then, then the track and field oval will become wet and
slippery.
If the track and field oval will become wet and slippery, then the track and
field game will be cancelled.
2. If you are resting, then you will be relaxed.
If you are relaxed, then your heart beat is normal.
3. If you study your lesson, then you will pass the exam.
If you pass the exam, you will get a good grade.
4. If it creature is a fly , then it has and antennae.
If the creature has antennae, then it is an insect.
5. If you are studying science, then you are studying biology.
If you are studying biology, then you are studying botany.
6. If two lines are parallel, then they belong to one plane.
If lines belong to one plane, then they are coplanar.
7. If angles are linear pair, then they are supplementary angles.
If the angles are supplementary, the sum of the angles is 1800.
8. If a man is good in Math, then he is an engineer.
If he is an engineer, then he can build a house.
9. If a creature is a mammal, then it has 2 legs.
If a creature has 2 legs, then it can swim
10. If it rain, then there is lightning
If there is lightning, then there is thunder.
*I-I need help HUHU*
non-sense answers; auto report
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Answers & Comments
Answer:
A.
1. Reason:
2. Definition of odd integer
3. Definition of even integer
5. sum of integers
2. mn = (2k + 1)(2k)
= 4k2 + 2k product of integers
= 2(2k2 + k) factor out 2
= 2r
let r = 2k2 + k mn = 2r
by definition of even integer
3. let n = 2k
3n + 5 = 3(2k) + 5
by substitution
= 6k + 5 multiply
= 6k + 4 + 1 renaming 5
= 2(3k + 2) + 1 factor out 2
= 2m + 1
let m = 3k + 2
3n + 5 = 2m + 1
is odd number by definition.
B. 1. Given x = 3
Prove : 3x + 5 ≠ 10 Assume that 3x + 5 = 10
3x = 5
x = 5/3 This shows that the assumption is not true. Hence the conclu-sion 3x + 5 ≠ 10 is true.
2. Given: Triangle ABC is an isosceles triangle.
Prove: Base angle cannot be 920.
Assume that the base angle is 920 Remember that the base angles of isosceles triangle are equal and the sum of the measure of the angles of the triangle is 1800 A + B + C = 1800 A + 92 + 92 = 1800 This is not possible since the two angles adds up to more than 1800 already.
Therefore the assumption is false.
The conclusion that cannot be 920 is true.
3. Given: 3r - 5 ≠ 13
Prove: r ≠ 6 Assume that r = 6. Then 3( 6) - 5 ≠ 13
18 - 5 ≠ 13 this false be-cause they are equal.
Hence the assumption is false. r ≠ 6 is true. 4. Given: x = 5
Prove: 2x + 4 ≠ 12 Assume that 2x + 4 = 12 2(5) + 14 =12
10 + 14 = 12 is false Hence the conclusion 2x + 4 ≠ 12 is true.
Pa brainliest please.
P=two lines are parallel
Q=they do not intersect
Lines j and k are parallel