If x and y are real numbers and if xy=0, then either x=0 or y=0 Give...
Prove that x^2+xy+y^2≥0 for all real numbers, x and y. Find the values that result in equality.
For all real numbers x and y, if x is not equal to y, x>0,y>0 then (x/y)+(y/x)>2
For each of the following relations on the set of all real numbers, decide whether or not the relation is reflexive, symmetric, antisymmetric, and/or transitive. Give a brief explanation of why the given relation either has or does not have each of the properties. (x, y) elementof R if and only if: a. x + y = 0 b. x - y is a rational number (a rational number is a number that can be expressed in the form a/b...
Prove that for any two real numbers x and y, |x + y| ≤ |x| + |y|. Hint: Use the previously proven facts that for any real number a, |a|≥ a and |a|≥−a. You should need only two cases.
[9] Given any two real numbers x and y such that x < y, show that there exists a rational number q such that x < a <y.
A. Let x and y be two real numbers such that y - 2x = 20 and (3 - x)(y + 2) is a maximum. Find x and y. B. Suppose that one of these numbers is 6 what is the second one? Why?
Suppose R is the relation defined on all real numbers by for all real numbers x,y (xRy if |x-yl3) Then for real numbers x and y, xR2y iff
Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1. That is, x + y = 1. Given this constraint, which of the following functions of x is equivalent to the original function f(x,y)=xy? $$ \begin{aligned} &\tilde{f}(x)=1-x \\ &\tilde{f}(x)=x-x^{2} \\ &\tilde{f}(x)=x+x^{2} \\ &\widetilde{f}(x)=x^{2} \end{aligned} $$The langrange method can also be used to solve this constrained maximization problem.The langrangian for this constrained maximization problem is _______ Which of the following are the first order conditions for a critical...
Hello, I need help with the following Discrete problem, thank you! 2. Find real numbers x and y satisfying LY J LX J = LYX J - 1 3. Give examples of functions f and g such that f•g is onto, but g is not onto.
7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z 7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z