## What is wrong with the following “proof” that -3 = 3, using backward reasoning? Assume that -3 = 3. Squaring both sides yields (-3)2 = 32, or 9 = 9. Therefore -3 = 3

What is wrong with the following “proof” that -3 = 3, using backward reasoning? Assume that -3 = 3. Squaring both sides yields (-3)2 = 32 or 9 = 9. Therefore – 3 = 3. EXPERT ANSWER Yes, It is wrong.Because, even if the squares of two numbers equal then the two number ay not …

## 1.Use a proof by cases to show that 27 is not the square of a positive integer. 2, Use a proof by cases to show that 29 is not the square of a positive integer

1.Use a proof by cases to show that 27 is not the square of a positive integer. 2, Use a proof by cases to show that 29 is not the square of a positive integer EXPERT ANSWER

## Let A and B be sets. Show that a) (A ∩ B) ⊆ A. b) A ⊆ (A ∪ B). c) A − B ⊆ A. d) A ∩ (B − A) = ∅. e) A ∪ (B − A) = A ∪ B please show all your steps

Let A and B be sets. Show that:  (A ∩ B) ⊆ A.  A ⊆ (A ∪ B).  A − B ⊆ A.  A ∩ (B − A) = ∅.  A ∪ (B − A) = A ∪ B. EXPERT ANSWER a) To show that (A ∩ B) ⊆ A, we need to prove that …