Use the numbers 2,3 and 7 to verify the following properties of whole numbers under addition:
1) Closure. 2) Associativity.
3) Commutativity.
4) 0 is an additive identity
Answers
The numbers show closure, commutative and associative properties.
Closure:
If a set has a particular type of Numbers then the addition of those Numbers will result in the same type of number.
Such as,let us consider a set consisting of odd numbers {2,3,7}
These are odd numbers.
Hence,if we add them the result will be an odd number.
I.e.,2+3+7=12 which is an odd number.
Therefore, the given triplets satisfy the closure rule.
Commutative rule:
According to this rules if three numbers are taken as A,B,C then
Either (A+B)+C=A+(B+C)(Commutative addition)
Or (A*B)*C=A*(B*C)
Putting A,B,C as 2,3,7 we see they satisfy the given relations.
Associative property:
According to this property,
A+B=B+A (Associative addition)
A*B=B*A(Associative multiplication)
Putting A and B as 2,3,7 alternatively we see they satisfy Associative property.
0 is an additive identity:
It states that adding a number to zero won't change the number.
The number will stay the same as before.
2+0=2
3+0=3
7+0=7
Hence they satisfy Identity property.