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Learning task 3
A. Prove the following using direct proof
B. Prove the following using indirect proof​

Learning Task 3A Prove The Following Using Direct ProofB Prove The Following Using Indirect Proof class=

Sagot :

betachan16

Answer:

A.

2. Definition of odd number

3. Definition of even number

5. Adding like terms in statement 4, 2k + 2k = 4k or 2(2k)

B.

1. Given : x = 3

1. Given : x = 3Prove : 3x + 5 ≠ 10

1. Given : x = 3Prove : 3x + 5 ≠ 10Assume that 3x + 5 = 10

1. Given : x = 3Prove : 3x + 5 ≠ 10Assume that 3x + 5 = 103x = 5

1. Given : x = 3Prove : 3x + 5 ≠ 10Assume that 3x + 5 = 103x = 5x = 5/3

1. Given : x = 3Prove : 3x + 5 ≠ 10Assume that 3x + 5 = 103x = 5x = 5/3Assumption is not true. The conclusion 3 + 5 ≠ 10 is true

2. Given : Triangle ABC is an is an isosceles triangle

2. Given : Triangle ABC is an is an isosceles triangleProve : Base angle cannot be 92 degrees

2. Given : Triangle ABC is an is an isosceles triangleProve : Base angle cannot be 92 degreesAssume that the base angle is 92 degrees

2. Given : Triangle ABC is an is an isosceles triangleProve : Base angle cannot be 92 degreesAssume that the base angle is 92 degreesA + B + C = 180 degrees

2. Given : Triangle ABC is an is an isosceles triangleProve : Base angle cannot be 92 degreesAssume that the base angle is 92 degreesA + B + C = 180 degreesA + 92 + 92 = 180 degrees

2. Given : Triangle ABC is an is an isosceles triangleProve : Base angle cannot be 92 degreesAssume that the base angle is 92 degreesA + B + C = 180 degreesA + 92 + 92 = 180 degreesThis is not possible since the two angles adds up to more than 180 degrees already. Therefore the assumption is false. In conclusion it is true that the base angle can not be 92 degrees

3. Given : 3r - 5 ≠ 13

3. Given : 3r - 5 ≠ 13Prove : r ≠ 6

3. Given : 3r - 5 ≠ 13Prove : r ≠ 6 Assume that r = 6

3. Given : 3r - 5 ≠ 13Prove : r ≠ 6 Assume that r = 6Then 3(6) - 5 ≠ 13

3. Given : 3r - 5 ≠ 13Prove : r ≠ 6 Assume that r = 6Then 3(6) - 5 ≠ 1318 - 5 ≠ 13 is false because they are equal.

3. Given : 3r - 5 ≠ 13Prove : r ≠ 6 Assume that r = 6Then 3(6) - 5 ≠ 1318 - 5 ≠ 13 is false because they are equal.Hence the assumption is false r ≠ 6 is true

4. Given : x = 5

4. Given : x = 5Prove : 2x + 4 ≠ 12

4. Given : x = 5Prove : 2x + 4 ≠ 122(5) + 14 = 12

4. Given : x = 5Prove : 2x + 4 ≠ 122(5) + 14 = 12Assume that 2x + 4 = 12

4. Given : x = 5Prove : 2x + 4 ≠ 122(5) + 14 = 12Assume that 2x + 4 = 122 (5) + 14 = 12

4. Given : x = 5Prove : 2x + 4 ≠ 122(5) + 14 = 12Assume that 2x + 4 = 122 (5) + 14 = 1210 + 14 = 12 is false

4. Given : x = 5Prove : 2x + 4 ≠ 122(5) + 14 = 12Assume that 2x + 4 = 122 (5) + 14 = 1210 + 14 = 12 is falseHence the conclusion 2x + 4 ≠ 12 is true

Step-by-step explanation:

Hope it helps!

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