[SOLVED] CSE211 - Homework 2

Description

Problem 1: Sets                                                                                                                                         

Which of the following sets are equal? Show your work step by step.

• {t : t is a root of x² – 6x + 8 = 0}
• {y : y is a real number in the closed interval [2, 3]}
• {4, 2, 5, 4}
• {4, 5, 7, 2} – {5, 7}
• {q: q is either the number of sides of a rectangle or the number of digits in any integer between 11 and 99}

(Solution)

1

– Homework #2                                                                                                                                                                                        2

Problem 2: Cartesian Product of Sets                                                                                                                      (15 points)

Explain why (A × B) × (C × D) and A × (B × C) × D are not the same.

(Solution)

(25 points)

Let A, B and C be sets which have different cardinalities. Let (p, q, r) be each triple of A × B × C where p ∈ A, q ∈ B and r ∈ C. Design an algorithm which finds all the triples that are satisfying the criteria: p ≤ q and q ≥ r. Write the pseudo code of the algorithm in your solution.

For example: Let the set A, B and C be as A = { 3, 5, 7 }, B = { 3, 6 } and C = { 4, 6, 9 }. Then the output should be : { (3, 6, 4), (3, 6, 6), (5, 6, 4), (5, 6, 6) }.

(Note: Assume that you have sets of A, B, C as an input argument.)

(Solution)

for write a condition do

end

When you want to write a while loop, you can use:

while write a condition do

If you need to return, use return end

For any additional things you have to do while writing your pseudo code, Google ”How to use algorithm2e in Latex?”.

– Homework #2                                                                                                                                                                                        3

Problem 4: Relations                                                                                                                    (3+3+3+3+3+3+3=21 points)

Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if (a) x 6= y.

(Solution)

• xy ≥ 1.

(Solution)

• x = y + 1 or x = y – 1.

(Solution)

• x is a multiple of y.

(Solution)

• x and y are both negative or both nonnegative.

(Solution)

• x ≥ y². (Solution)
• x = y².

(Solution)

Let f be the function from R to R defined by f(x) = x². Find

(a) f⁻¹ ({ x | 0 < x < 1 })

(Solution)

(b)f⁻¹ ({ x | x > 4 })

(Solution)