Explanation:

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.

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.