(2) x + 1 is even -> x^2 is odd
(hint: use a direct proof)
(a) (0.5 points) What are you assuming is true:
(b) (0.5 points) What are you proving is true:
(c) (1 point) Complete the proof:
QUESTION 6 1. 2 Give a direct proof that if n' is even, then n is even. [Hint: Consider whether n? +n is odd or even and from that whether n is odd or even.]
please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
1. Prove with a direct proof or disprove by counterexample. If x is an odd integer, then x3 is an odd integer.
Show that if a is odd and 3a+3b is even then b is odd and ab is odd by 1) Direct Proof 2) Proof by contradiction
3) [3 marks] Use a proof by cases that for all real number x, xs]x]. You may need this definition. For any real numbers x, [x]= x, if x2 0, -x, otherwise. 4) [3 marks] Give a direct proof that If x is an odd integer and y is an even integer, then x + y is odd. 5) [3 marks] Give a proof by contradiction for the proposition in Q4, above. That is, give a proof by contraction for...
1. Determine if v(t) = t^2 (t-squared) is an even or odd function. Show your proof. 2. Determine if v(t) = t^2 (t-squared) is an even or odd function. Show your proof. 3.A sinusoidal signal has a period of 10 ms. What is the angular frequency? 4.A sinusoidal signal has a period of 10 ms. What is the angular frequency?
Use the method of direct proof to prove the following statement: For integers a and b, if a is odd or b is odd, then (a + 7)(b 5) is even.
2) (3 points; J2) The function below is even, odd, or nelther even nor odd. Select the statement below which best describes which it is and how you know. f(x) = 5 x6 - x2 + 8 A) This function is even because f(-x) = f(x). B) This function is odd because f(-x) = -f(x). C) This function is even because f(-x) = -f(x). D) This function is odd because f(-x) = f(x). E) This function is neither even nor...
Discrete Mathematics. (a) Use the method of generalizing from the generic particular in a direct proof to show that the sum of any two odd integers is even. See the example on page 165 of the 5th edition of Discrete Mathematics with Applications, Metric Version for how to lay this proof out. (b) Determine whether 0.151515... (repeating forever) is a rational number. Give reasoning. (c) Use proof by contradiction to show that for all integers n, 3n + 2 is...
Part H. Direct Proof. Construct a direct proof for the following argument. Use no assumptions. The pro completed in the number of steps indicated. [6 points) 40. 1. A 2. A -Z → (B → Z) :~B