Advanced Math

1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the sum of two even integers is even. 3. Show that the square of an even number is an even number using a direct proof. 4. Show that the additive inverse, or negative, of an even number is an even number using a direct proof. 5. Prove that if m+n and n+p are even integers, where m,n, and p are integers, then m+p is even. What kind of proof did you use? 6. Use a direct proof to show that the product of two odd numbers is odd. 7. Use a direct proof to show that every odd integer is the difference of two squares. 8. Prove that if n is a perfect square, then n+2 is not a perfect square.

Mathematics, Advanced Math / By

EXPERT ANSWER

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

Mathematics, Advanced Math / By

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 …

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 Read More »

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

Mathematics, Advanced Math / By

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 …

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 Read More »