Prove the given statement about subsets A and B of Rⁿ, or provide the required example in R². A proof for an exercise may use results from earlier exercises (as well as theorems already available in the text).

Find an example in R² to show that equality need not hold in the statement of Exercise 31.

Data From Exercise 31.

Prove the given statement about subsets A and B of Rⁿ, or provide the required example in R². A proof for an exercise may use results from earlier exercises (as well as theorems already available in the text).

[(aff A) ∪ (aff B)] ⊆ aff (A ∪ B). To show that D ∪ E ⊆ F, show that D ⊆ F and E ⊆ F.]