Consider the equivalence relation R={(x,y)|c-y is an integer}. a) What is the equivalence class of 1 for this equivalence relation? b) What is the equivalence class of 1/2 for this equivalence relation?

Do patients with COPD have the same level of therapuetic effect of bronchodialators?

Which of these are partitions of the set Z × Z of ordered pairs of integers? a) the set of pairs (x, y), where x or y is odd; the set of pairs (x, y), where x is even; and the set of pairs (x, y), where y is even b) the set of pairs (x, y), where both x and y are odd; the set of pairs (x, y), where exactly one of x and y is odd; and the set of pairs (x, y), here both x and y are even c) the set of pairs (x, y), where x is positive; the set of pairs (x, y), where y is positive; and the set of pairs (x, y), where both x and y are negative d) the set of pairs (x, y), where 3 | x and 3 | y; the set of pairs (x, y), where 3 | x and 3 ✗y; the set of pairs (x, y), where 3 ✗ x and 3 | y; and the set of pairs (x, y), where 3 ✗ x and 3 ✗ y e) the set of pairs (x, y), where x > 0 and y > 0; the set of pairs (x, y), where x > 0 and y ≤ 0; the set of pairs (x, y), where x ≤ 0 and y > 0; and the set of pairs (x, y), where x ≤ 0 and y ≤ 0 f) the set of pairs (x, y), where x ≠ 0 and y ≠ 0; the set of pairs (x, y), where x = 0 and y ≠ 0; and the set of pairs (x, y), where x ≠ 0 and y = 0.

Let $A=\mathbb{N} \times \mathbb{N}$, and define a relation R on A by (a, b) R (c, d) iff $a^{b}=c^{d}$. (a) Show that R is an equivalence relation on A. (b) List the elements in the equivalence class $E_{(9,2)}$. (c) Find an equivalence class with exactly two elements. (d) Find an equivalence class with exactly four elements.

An equivalence relation is any relationship that satisfies the Reflexive, Symmetric, and Transitive Properties. For real numbers, equality is one type of equivalence relation. Determine whether each relation is an equivalence relation. Explain your reasoning. ≈,for the set of real numbers

Which of these collections of subsets are partitions of {1, 2, 3, 4, 5, 6}? a) {1, 2},{2, 3, 4},{4, 5, 6} b) {1}, {2, 3, 6}, {4}, {5} c) {2, 4, 6}, {1, 3, 5} d) {1, 4, 5}, {2, 6}

Determine whether the given relation is an equivalence relation on {1, 2, 3, 4, 5, }. If the relation is an equivalence relation, list the equivalence classes. {(x,y)| x divides 2-y}

Find the smallest equivalence relation on the set {a, b, c, d, e} containing the relation {(a, b), (a, c), (d, e)}.

What is the congruence class [4]ₘ when m is a) 2? b) 3? c) 6? d) 8?

True/False. All classes are derived from the Object class.

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Explain why a golf ball is heavier than a table-tennis ball, even though the balls are the same size

Indicate whether the statement is true or false. Give a reason for your choice. A parley might lead to peace between warring factions.

Suppose that A is a nonempty set, and f is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs (x, y) such that f(x) = f(y). a) Show that R is an equivalence relation on A. b) What are the equivalence classes of R?