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Consider real numbers a, b, c, d, and e satisfying the following inequalities: a > c, d > b, c > e, d > a, and b > c . Based solely on these relationships, which of the following pairs has no established order?

Explanation	Calculations	Help
$We first note all the given inequalities.$	$a > c d > b c > e d > a b > c$
$We chain the inequalities to compare a and e.$	$a > c and c > e implies a > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare d and e.$	$d > a and a > c and c > e implies d > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare d and c.$	$d > a and a > c implies d > c$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare b and e.$	$b > c and c > e implies b > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We compare a and b and see that both are greater than c, but their relationship to each other is not determined.$	$a > c and b > c Neither a > b nor b > a can be concluded$

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A

Consider real numbers a, b, c, d, and e satisfying the following inequalities: a > c, d > b, c > e, d > a, and b > c . Based solely on these relationships, which of the following pairs has no established order?

Explanation	Calculations	Help
$We first note all the given inequalities.$	$a > c d > b c > e d > a b > c$
$We chain the inequalities to compare a and e.$	$a > c and c > e implies a > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare d and e.$	$d > a and a > c and c > e implies d > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare d and c.$	$d > a and a > c implies d > c$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We chain the inequalities to compare b and e.$	$b > c and c > e implies b > e$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We compare a and b and see that both are greater than c, but their relationship to each other is not determined.$	$a > c and b > c Neither a > b nor b > a can be concluded$

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A