Part 1:
The Symmetric Property of Equality states that if a = b then b = a.
Given that if 43 = y, then y = 43, the mathematical property shown by the statement is the symmetric property.
Part 2:
The associative property states that you can add or multiply regardless of how the numbers are grouped.
The associative property of multiplication states that a * (b * c) = (a * b) * c.
Thus, given that (4y * 9) * 7 = 4y * (9 * 7), the mathematical property shown by the statement is the associative property of multiplication.
Part 3:
The set of natural numbers is the set of integers starting from 1, 2, . . .
Notice that the addition of any two natural numbers always gives you a natural number while the subtraction of two natural numbers does not always result in a natural number.
i.e. consider the natural numbers 5 and 6, 5 - 6 = -1 and -1 is not a natural number.
Therefore, the true statement about the set of natural numbers is "the set is closed under addition and not closed under subtraction".
