Complete the following direct proof of the statement: If x and y are positive real numbers and x < y, then x² < y²2². Hint: answer each blank with an expression. Type "x^2" for "x2" proof. Since x/y Since Since x² < Hint: , multiply both sides of x < y by x yields " mutiply both sides of x < y by y yields <2²₁x² <2².0
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- Suppose that p and q are statements so that p → q is false. Find the truth values of each of the following. (a) ~p → q TrueFalse (b) p ∨ q TrueFalse (c) q → p TrueFalseWrite the following compound statement in terms of the simple statements p, q, and r. "I go to office hours and ask questions, and my professor does not remember me." p: I go to office hours. q: I ask questions. r: My professor remembers me.Tell if the statements are true or false. Let p: 2 + 1 = 3; q: 16 − 9 = 7. (a) ~p ∨ q TrueFalse (b) ~p ∧ ~q TrueFalse (c) ~(p ∧ q) TrueFalse
- Let p = “Sophie has been arrested” and q = “Bubba’s never been arrested.” Write the symbolic form of You’re saying that Sophie’s been arrested? That is totally not true. (A) ~q (B) p (C) ~(~p) (D) ~pAnswer this question: Write it with pencil and show how you solved it Write the truth table for the following statement forms a. P Λ ( ~ q V r) b. (P Λ ~ q) Λ (q V ~r)Determine the truth value of the statement (~p ∨ q) ∨ (r ∧ q) using the following conditions. a) p is false, q is true, and r is true. b) p is true, q is false, and r is false. a) If p is false, q is true, and r is true, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False? b) If p istrue, q is false, and r is false, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False?
- Let p, q, and r represent the following statements: p: The first ball is red. q: The second ball is white. r: The third ball is blue. Which would be the correct English statement for the symbolic form (¬¬p ∧∧ q) →→ r ? Group of answer choices A .If the first ball is red or the second ball is white, then the third ball is blue. B. If the first ball is not red or the second ball is white, then the third ball is blue. C .If the first ball is not red and the second ball is white, then the third ball is blue. D. If the first ball is red and the second ball is white, then the third ball is blue.When you use a mortgage to purchase a home, the lending institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k) = P((1 + r)k − 1) (1 + r)t − 1 dollars. In this exercise, assume that the mortgage amount is $200,000, the APR is 6% so r = .06/12 and the term of the loan is 30 years (360 months). (a) Find a formula for the equity. (b) Make a graph of the equity over 360 months, the term of the loan. (c) Does the graph show that you have half-ownership in the home halfway through the term of the mortgage? Halfway through the term of the mortgage corresponds to k1 = _______ payments. From the graph, we see that E(k1) is ________ half of the mortgage amount, so we _______ have half-ownership in the home…Write one of each of the following statements. They must be entirely unique, not from thetextbook, the internet or class examples. Include examples that are relevant to you.a) A statement using a conjunction and how you know when that statement is true.b) A statement using a negation.c) A statement using a disjunction.d) A conditional statement and how you know when that statement is falsee) A biconditional statementf) A statement that contains a quantifier and the negation of that statement.
- please help me to solve this filling blank question? paython 10. x=2.4, a=7.5,y=8. The expression x+a%3*(int)(x+y)%2//4 is _______________.For what values of x is the following if statement true? int y = 10; int x; if (( x / y == 1) && ( x % 2 == 1 )){ doSomething(); }Rewrite each of the following statements in the form “If A, then B.”a. Candidate Lu winning the election will be a sufficient condition for property taxes to increase.b. The user clicks Pause only if the game level changes.c. The components are scarce, therefore the price increases.d. Healthy hair is a necessary condition for good shampoo.