(1) State whether or not each of the following sets are equal, equivalent, or infinite.

(a) X = {3, 6, 9, ...}
(b) A = {2, 4, 6} and {4, 6, 2}
(c) P = {l, m, n} and {1, 5, 9}

(2) Simplify:

(a) -7x × 2y
(b) -18x(-3)
(c) 7y - 8y

Let's address each part of the question step-by-step:
(1) Determine if sets are equal, equivalent, or infinite:
(a) X = {3, 6, 9, ...} :

This set continues indefinitely by adding 3 to each previous number.

Conclusion : This set is infinite because it has no end.


(b) A = {2, 4, 6} and {4, 6, 2} :

Both sets contain the same elements: 2, 4, and 6.

Order doesn’t matter in sets.

Conclusion : These two sets are equal because they contain the same elements.


(c) P = {l, m, n} and {1, 5, 9} :

The first set contains the elements l, m, and n, which appear to be letters, while the second set contains the numbers 1, 5, and 9.

They don’t share any elements.

Conclusion : These sets are neither equal nor equivalent since they have different elements and types of elements.


(2) Simplify each expression:
(a) − 7 x × 2 y :

To simplify, multiply the coefficients (-7 and 2).

− 7 × 2 = − 14 , so the simplified expression is − 14 x y .


(b) − 18 x ( − 3 ) :

Multiply the coefficients (-18 and -3).

− 18 × − 3 = 54 , so the simplified expression is 54 x .


(c) 7 y − 8 y :

Combine like terms by subtracting the coefficients of y.

7 y − 8 y = − y , so the simplified expression is − y .


These simplifications and set analyses help clarify the concepts of set equality and operations on algebraic expressions.

Answered by OliviaMariThompson | 2025-07-06