DISCRETE STRUCTURES

CPSC-50200

DISCRETE STRUCTURES

Fall 2018

Homework 7

Due Date: Monday, 10/15/2018

Provide your answers on this document, and submit back to blackboard either in WORD or PDF format. WORD provides tools for using formulas, select the Insert Tab, then click on Equation, then scroll down to select New Equation, you will see the different symbols and notations on the top, where you can make your own formulas.

Q1) (20 points) Providing the definition: .

Use mathematical induction to prove that , .

Providing the definition: Cn=1^2+2^2+3^2+….+n^2

Use mathematical induction to prove that , .

Q2) (10 points) Use proof by contradiction to prove the proposition: If −2a+7 is even, then a is odd. Suppose a ∈ Z.

3) (10 points) Use Direct proof to prove the claim

Claim: If d = min {, } and x ≤ d, then x ≤ and x ≤ .

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