Property vs. element

[azajewel]

I have no idea what the term property and element mean. Can someone help me? I've eliminated the answers 3 and 4, but not sure which is correct, 1 or 2.

6+(3+2)=6+5 illustrates the:
1.distributive property
2.identity element of addition
3.substitution property
4.closure property of addition and multiplication

 

[mmm4444bot]

I have no idea what the term property and element mean.

Where do you see the word "element" ?

I mean, how is it used ?


6 + (3+2) = 6 + 5 illustrates the:

1.distributive property Nope.

The Distributive Property always involves multiplication.


2.identity element of addition Nope.

The additive identity is zero. There's no zero, in your equation.

3.substitution property This is correct.

If you see the expression 3+2 somewhere, you can replace it with 5 because both expressions are the same number. When you replace the expression 3+2 with the expression 5, we say that you have "substituted 5 for 3+2".

I suppose the substitution property says something like, "You can substitute anything for anything, as long as they're both equal."

4.closure property of addition and multiplication Nope.

The closure properties just say that, if you're adding or multiplying Real numbers, then you're gonna end up with a Real number.

 

[Denis]

I have no idea what the term property and element mean.

WHY were you given the problem then?

 

[mmm4444bot]

2.identity element of addition

I just found it.

Here, the phrase "identity element" refers to the number zero.

Choice #2 is a property also. It's the property of zero that says zero has no value; adding zero to something adds nothing.

Here's another property that is similar, but for multiplication.

The multiplicative identity says that the "identity element of multiplication" is 1.

Multiplying something by 1 does not change anything.

So, "property" is a statement, and "element" is a noun.

Cheers!