Question

13. Express -8' as the sum of a negative integer and a whole number.
14. Give the general form of Clasure, Commutative, Associative under Addition and
give examples on your own.
15. (2 + 5) + 4 = 2 + (5 + 4) does the associative property hold for whole numbers?
Take two more examples and write your answer.
16. Take at least five different pair of integers and see if subtraction is Commutative.
17. Take at least five different pair of integers and see if subtraction is Associative.​

Answer 1

Answer:

13. 1 and -9.

Explnatation: 1+(-9)=1-9=-8

14. Closure: x+y= an integer if x and y are integers. Ex: 1+2=3

Commutative: x+y=y+x. Considering both are positive integers. Ex: 5+3=3+5=8

Associative under addition: x+(y+z)=(x+y)+z. Ex: 1+(2+3)=(1+2)+3=6

15. Yes the Associative property does hold true for whole numbers.

This can be explained using the given example:

(2+5)+4=2+(5+4)

(2+5)+4=7+4=11

2+(5+4)=2+9=11

Ex1: 6+(7+8)=(6+7)+8

6+(7+8)=6+15=21

(6+7)+8=13+8=21

Ex2: 9+(5+4)=(9+5)+4

9+(5+4)=9+9=18

(9+5)+4=14+4=18

16.

1) 5-3=2 ; 3-5=-2

2) 7-9=-2 ; 9-7=2

3) 16-3=13 ; 3-16=-13

4) 7-3=4 ; 3-7=-4

5) 20-8=12 ; 8-20=-12

Hence subtraction is not commutative as shown in the examples above. Since the result of subtraction changes when the order of the integers is changed.

17.

1) 5-(3-1)=3 ; (5-3)-1=1

2) 7-(9-8)=6 ; (7-9)-8=-10

3) (16-3)-13=0 ; 16-(3-13)=26

4) (7-3)-4=0 ; 7-(3-4)=8

5) (20-8)-12= 0 ; 20-(8-12)= 24

Hence subtraction is not associative as shown in the examples above. Since the result of subtraction changes when the order of subtracting the integers is changed.

Hope this answer helped :)