Question

given that a=(-10),b=7 and c=(-3), verify that addition is communicative and associative. Also show that subtraction is neither communicative nor associative.​

Answer 1

in commutative law we can change the order of numbers as 10+20=20+10 and the result is same.

in associative law we can associate any two or more numbers with each other for ease of calculation as 20+(10+15)=(20+10)+15 the answer is same 45

Verification of commutative law

a+b+c= -10+7+-3= -6

or b+a+c= 7+ -10+ -3=6

Verified

Verification of associative law

a+(b+c)= -10+(7+-3)= -10 + 4= -6

or (a+b)+c= (-10+7)+ -3= -3+ -3= -6

Verified

In case of subtraction

Commutative law does not hold

a-b-c not equals to c-a-b

as -10-7- -3= -14

while -3- -10 -7=7-7=0

For associative law

a-(b-c) not equals to (a-b)-c

as -10-(7- -3)= -10-10= -20

(a-b)-c= (-10-7)- -3= -17 + 3 = -14