A list of utility functions appears below. For each one sketch the corresponding upper contour

set and determine which ones are convex. Where an upper contour set is not convex, indicate

by identifying two points in the set with the property that a portion of the straight line between

them lies outside the upper contour set.

U (x₁, x₂₎ = min {x₁, x₂}

U (x₁, x₂) = max {x₁ , x₂}

U (x₁, x₂) = x₁+x₂

U(x₁, x₂) = x₁+ x₂^0.5

U(x₁, x₂) = 2x₁+ 2x₂+ 3

Identify any pairs of utility functions that represent the same preferences.