For the following pairs of sets, state which of these statements is true: "A is a subset of B", "B is a subset of A", "A is a proper subset of B", "B is a proper subset of A". It’s possible for multiple statements to be true, or none of them. a. A = {3, +√5 2 − 4 2, √27 3 }, B = {3,{3},{3}} b. A = {{1, 2},{2, 3}},B = {{1, 2, 3}} c. A = {1, 2, 3},B = {{1},{2},{3}} d. A = {√16,{4}} , B = {4}

a. A = {3, +√5 2 − 4 2, √27 3 }, B = {3,{3},{3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

b. A = {{1, 2},{2, 3}},B = {{1, 2, 3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

c. A = {1, 2, 3},B = {{1},{2},{3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

d. A = {√16,{4}} , B = {4} (B is a proper subset of A)

All elements of B i.e. 4 is present in set A with an additional element also there in A i.e. {4}

2x + 4y = 28

-2y = x + 28

Step-by-step explanation:

Looking at the graph, we can see that the lines do not intersect. Therefore, they do not have a shared solution. We need to find the system of equations that does not have a solution.

1) Let's try to solve the third system given (counting from the top). To solve with the substitution method, we need to isolate one variable in one of the equations. I chose to isolate y in -2y = x + 28:

2) Now that we've isolated the y in that equation, substitute what y equals in that equation for the y in the other equation. So, substitute for y in 2x + 4y = 28 and simplify:

In a normal situation, the x's would not cancel out, and we would be able to isolate x to get the x-value of the solution. However, in this case, they have, and we ended up with a false statement, as -64 does not equal 28. Whenever this happens, it means the system does not have a solution. Therefore, the third option would represent the system in the graph.