1. Proof the following statement: I a) Let x E R. If x > 0, then x² + 2 > 0 b) Suppose n € Z. If n² < 0, then n is positive or negative number. c) Proof that 5X +3 is even if and only if X is odd.
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Max Function
Statistical function is of many categories. One of them is a MAX function. The MAX function returns the largest value from the list of arguments passed to it. MAX function always ignores the empty cells when performing the calculation.
Power Function
A power function is a type of single-term function. Its definition states that it is a variable containing a base value raised to a constant value acting as an exponent. This variable may also have a coefficient. For instance, the area of a circle can be given as:
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- Determine whether the following argument is valid or invalid. Include a truth table and a few words explaining why the truth table shows validity or invalidity. Use the space provided below to draw the truth table If Hugo is a physics major or if Hugo is a math major, then he needs to take calculus. Hugo needs to take calculus or Hugo is a math major. Therefore, Hugo is a physics major or Hugo is a math major.Exercise 1.1.4: Truth values for statements with inclusive and exclusive or. infoAbout Indicate whether each statement is true or false, assuming that the "or" in the sentence means the inclusive or. Then indicate whether the statement is true or false if the "or" means the exclusive or. (a) February has 31 days or the number 5 is an integer. (b) The number π is an integer or the sun revolves around the earth. (c) 20 nickels are worth one dollar or whales are mammals. (d) There are eight days in a week or there are seven days in a week. (e) January has exactly 31 days or April has exactly 30 days.Modified coin-row problem:If we modified the coin-row problem, so that you cannot take the adjacent coin, and youcannot take the coin next to the adjacent coin also (see example below), what would thedynamic programming formula F(n) be?Example: A, B, C, D, E, F, G, H, I, JIf A is taken, then B & C cannot be taken, but D (or above D, like E and so on) can be taken.If B is taken, then A, C, D cannot be taken.And so on.
- Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b 2); The following two statements are logically equivalent (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True FalseDevelop problem-solving skills that generate idea creation, and apply them to everyday personal and professional experience. Instructions A syllogism is a type of logical argument that uses deductive reasoning to come to a conclusion. There are many types, but for this task, you will use a categorical syllogism. Categorical syllogisms: This type of syllogism assumes if A is a part of C, then B is a part of C (A and B are members of C). You can organize the syllogism in three sentences: 1. Your employer wants to promote a productive and logical work environment. To organize your thoughts and ideas in a coherent manner, you must practice your cognitive skills on a daily basis. To practice the process of creative problem solving, your boss has asked you to create two categorical syllogisms about a hypothetical everyday problem. For example, you are regularly late for work. 2. For your third and final syllogism, your boss wants you to introduce a new minor premise that would provide…Arithmetic and Logical Operators: Evaluate each of the following statements as True or False. Show intermediate steps for full credit. Try by simplifying only one operator at a time if the whole expression is dicult to understand. (SEE PHOTO) ______________________________________________________________________________ English to Logic (Lawn) Express each sentence using logical operations :, ^, _ and the propositional variables r; s; and l dened below. The use of the word "or" in the sentences below always means inclusive or. r it is raining l the lawn is wet s the sprinkler is on i) It is raining and the lawn is wet ii) It is not raining but the lawn is wet iii) The lawn is not wet and it is not raining iv) There is no way that it is raining v) It is raining or the sprinklers are on vi) Despite the fact that it is raining, the sprinklers are on Consider the eclectic animal collection at the local zoo. Express each sentence using logical operations and the propositional…
- ARGUMENT SEVEN Valid ☐ Invalid ☐ No J is B All B is K ∴ No K is J Convert the following argument into symbolic form and then determine whether it is a valid argument by using the Venn Diagram method (include the Venn Diagrams below). ARGUMENT EIGHT Valid ☐ Invalid ☐ No students in COSA 2 who showed up to class finished the reading. A few of them finished the training at home though. It stands to reason that some of the students who showed up to class did not finish the training. Write the argument in Symbolic Form: No M are R Some M are T Some M are not T Venn Diagrams: ARGUMENT NINE Valid ☐ ï Invalid ☐ Anything that is true is a statement and Professor Rosillo makes statements. So, all statements Professor Rosillo makes are true. Write the argument in Symbolic Form: Venn Diagrams:3. The formula for determining compound interest is: A represents the amount to earn; P is the principle that is initially invested; r is the interest rate earned; n is the number of times the interest is compounded; and t is the number of time periods for the investment. Write a program that prompts the user to enter P, r, n and t. The program should output the amount earned on the investment. 4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result.lQ: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices A): b→(s∧¬v) B): b→(s→¬v) C): s∧(¬v→b) D): (s∧¬v)→b
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