Q:

# which mathematical property is shown by each statement? 1) if 43=y, then y=432) (4y*9)*7=4y*(9*7)a. symmetric propertyb. transitive propertyc. associative property of additiond. reflexive property 3) which statement is true for the set of natural numbers? a. the set is closed under addition and closed subtraction b. the set is closed under subtraction and not closed under additionc. the set is not closed under addition and closed under subtraction d. the set is not closed under addition or subtraction

Accepted Solution

A:
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".