SolarMidnite
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Homework Statement
Using contradiction, prove that for every four positive real numbers c, d, e and f, at least one of c, d, e, f is
greater than or equal to the average of c, d, e, f.
Homework Equations
I don't believe that there are any relevant equations for this problem. I do know that we have to suppose that the negation of the statement is true, show that this supposition leads to a contradiction and then conclude that the statement to be proved is true.
The Attempt at a Solution
I am finding it difficult to translate the above statement into predicate logic because I have only worked with two variables and there are four in this problem! Here is my attempt but I think that I'm way off.
\forall (c \wedge d \wedge e \wedge f) \in ℝ+, \exists(c \vee d \vee e \vee f) \in ℝ+ \geq (c+d+e+f)/4
The negation in words might be something like: at least one of the four positive real numbers c, d, e and f will be less than the average of c, d, e, f.