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cassidipark

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The smallest and largest possible values of |A ∪ B| are 2, 4, and 6. The smallest and largest possible values of |A ∩ B| are 1, 0, and 1. The smallest and largest possible values of |A × B| are 6, 10, and 16.

6. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A ∪ B|? Explain. (b) What are the smallest and largest possible values of |A ∩ B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain.

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The smallest possible value of |A ∪ B| is 3 and the largest possible value is 18. The smallest possible value of |A ∩ B| is 0 and the largest possible value is 18. The smallest possible value of |A × B| is 4 and the largest possible value is 60.

6. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A ∪ B|? Explain. (b) What are the smallest and largest possible values of |A ∩ B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain.

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In the problem, we are given that there is a set called B with 5 members. We are also given that there is a set called A with 2, 4, 6, 8 members. We are also given that the intersection of these two sets is 5. We are also given that the union of these two sets is 18. We are also given that the difference of these two sets is 3. That is, the smallest possible value of A ∩ B is 1 and the smallest possible value of A × B is 4.

6. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A ∪ B|? Explain. (b) What are the smallest and largest possible values of |A ∩ B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain.

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A ∩ B = {x ∈ N : 3 ≤ x ≤ 13}
A ∪ B = {x ∈ N : x is even}
B ∩ C = {x ∈ N : x is odd}
B ∪ C = {x ∈ N : x is odd}

5. Let A = {x ∈ N : 3 ≤ x ≤ 13}, B = {x ∈ N : x is even}, and C = {x ∈ N : x is odd}. (a) Find A ∩ B. (b) Find A ∪ B. (c) Find B ∩ C. (d) Find B ∪ C.

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A ∩ B =
A ∪ B =

5. Let A = {x ∈ N : 3 ≤ x ≤ 13}, B = {x ∈ N : x is even}, and C = {x ∈ N : x is odd}. (a) Find A ∩ B. (b) Find A ∪ B. (c) Find B ∩ C. (d) Find B ∪ C.

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A class to represent a card in a card game. Cards are printed with the value and suit (e.g. 5D, 10C, JD, AS). Two cards are equal if they have the same suit and the same value. The class has two intl methods - equalSuit and equalValue - which compare two cards and return true if they are equal. The class has getters and setters.

Define a Java class for a card. This is the kind of card you have in a card game in that it has a value and a suit. Cards should b e printed as the value concatenated to the suit (e.g. 5D, 10C, JD, AS). Two cards are equal if they have the same suit and the same value. Include a metho d indicating if two cards have the same suit and another indicating if they have the same value. Call than equalSuit and equalValue resp ectively. Define getters and setters. You should submit a file named Card.java that contains the Card class. You should submit a file called App.java that contains main and tests all the capability of the card class. You should submit a text file with example input/output (from the terminal).

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A Java class to represent a card in a card game. The class has a value and a suit, and two cards are equal if they have the same suit and the same value. The class has getters and setters to access the value and suit. The class can be tested by running the tests file in the project.

Define a Java class for a card. This is the kind of card you have in a card game in that it has a value and a suit. Cards should b e printed as the value concatenated to the suit (e.g. 5D, 10C, JD, AS). Two cards are equal if they have the same suit and the same value. Include a metho d indicating if two cards have the same suit and another indicating if they have the same value. Call than equalSuit and equalValue resp ectively. Define getters and setters. You should submit a file named Card.java that contains the Card class. You should submit a file called App.java that contains main and tests all the capability of the card class. You should submit a text file with example input/output (from the terminal).

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A set of three squares is shown, each of which contains one of two different numbers. If the two numbers are added together, the result is the same as the number in the middle square. The two numbers in the middle square are both in set C.

Give an example of three sets A, B and C such that A B, B C, C * A, and C B.

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A, B, and C are all sets, but none of them is a subset of either of the other two sets.

Give an example of three sets A, B and C such that none of these three sets is a subset of either of the remaining two sets.

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The cardinality of set A is 34. The cardinality of set B is 36. The cardinality of set C is 1. The cardinality of set D is {;, {;}, {{;}}}

Determine the cardinality of each of the following sets. (a) A = {0, 2, 4, . . . , 34} (b) B = {35, 36, 37, . . . , 50} (c) C = {1, {1}, {1, 2}} (d) D = {;, {;}, {{;}}}

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The image accompanying this article will depict a set of dice. The first set contains six identical dice, while the second set contains one die that is different from the others.

Describe each of the sets below using words. (a) {n 2 Z : n 3 2 Z} (b) {. . . ,−5,−3,−1, 1, 3, 5, . . .}

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(a) The set of all integers whose absolute value is at most 5 is represented by a square with a cross in the center.
(b) The set of all natural numbers strictly between 1 and 10 is represented by a rectangle with a line running through the middle.

Describe each of the sets below using symbols. (a) The set of all integers whose absolute value is at most 5. (b) The set of all natural numbers strictly between 1 and 10.

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(a) The empty set.
(b) The set of all real numbers between −1 and 1.
(c) The set of all real numbers that are not zero.

Write each of the sets below by listing its elements. (a) A = {n 2 Z : n2 − n − 2 < 0} (b) B = {n 2 Z : −4 < n 4} (c) C = {x 2 R : x2 + 5 = 0}

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(a) If P and Q are both false, then ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) is true. If either P or Q are true, then ¬((¬P → ¬Q) ∧ (¬Q → R)) is false.

(b) If P and Q are both true, then ¬((¬P → ¬Q) ∧ (¬Q → R)) is true. If either P or Q are false, then ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) is false.

Use DeMorgan’s Laws, and any other logical equivalence facts you know to simplify the following statements. It would be a good idea to use only conjunctions, disjunctions, and negations. (a) ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) (b) ¬((¬P → ¬Q) ∧ (¬Q → R))

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For integers a and b, consider the biconditional: a + b is even if and only if 3a and 5b are even. This biconditional is true for some integers a and b, but false for others.

For integers a and b, consider the biconditional: a + b is even if and only if 3a and 5b are even. (a) Given an example for two distinct integers a and b for which this biconditional is true. (b) Given an example for two distinct integers a and b for which this biconditional is false.

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(b) (P →Q) → (Q →P)

(c) (P →Q) → (Q →¬P)

(a) (P →Q) → (¬P)
(b) (P →Q) → (Q →P)
(c) (P →Q) → (Q →¬P)

Let P and Q be statements. Construct a truth table for each of the following. (a) (P →Q) → (¬P)

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(a) T
(b) F

Let P and Q be statements. Construct a truth table for each of the following. (a) (P →Q) → (¬P) (b) (P ∧Q) ∧ (Q→ (¬P))

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A tautology is a statement that is always true. It is a contradiction to say that two statements are both tautologies.

Is (P ∧ (¬Q)) ∧ (P ∧Q) a tautology or contradiction?

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