Prove the following statements using either direct or contrapositive proof: Suppose x ∈ Z. If x³ - 1 is even, then x is odd.
Added by Nicol-S G.
Step 1
We are given that $x^3 - 1$ is even, which means it can be written as $2k$ for some integer $k$. So, we have $x^3 - 1 = 2k$. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 91 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Please use Proof by Contrapositive. Let x, y ∈ Z. Prove that if x - y is odd, then x and y are of opposite parity.
Sri K.
Write the first step in an indirect proof of the statement. (See Example 1.) If $x$ and $y$ are odd integers, then $x y$ is odd.
Relationships Within Triangles
Indirect Proof and Inequalities in One Triangle
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD