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learning task 3 a.prove the following using direct proof​

Learning Task 3 Aprove The Following Using Direct Proof class=

Sagot :

Betachan16idn

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

Prove : 3x + 5 ≠ 10

Assume that 3x + 5 = 10

3x = 5

x = 5/3

Assumption is not true. The conclusion 3 + 5 ≠ 10 is true

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

Prove : Base angle cannot be 92 degrees

Assume that the base angle is 92 degrees

A + B + C = 180 degrees

A + 92 + 92 = 180 degrees

This 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

Prove : r ≠ 6

Assume that r = 6

Then 3(6) - 5 ≠ 13

18 - 5 ≠ 13 is false because they are equal.

Hence the assumption is false r ≠ 6 is true

4. Given : x = 5

Prove : 2x + 4 ≠ 12

2(5) + 14 = 12

Assume that 2x + 4 = 12

2 (5) + 14 = 12

10 + 14 = 12 is false

Hence the conclusion 2x + 4 ≠ 12 is true

Step-by-step explanation:

Hope it helps!

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