5. Let ACR be a non-empty set that is bounded above, and x E R. Define...

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5. Let ACR be a non-empty set that is bounded above, and x E R. Define the set: (x+A) = {x+a: a Є A} (i.e. the set obtained by adding x to every element of A. For example, if A = {1,2,3} then (1+ A) = {2, 3, 4}.) Show that sup(x+4)=x+ sup(A). 5. Let ACR be a non-empty set that is bounded above, and x E R. Define the set: (x+A) = {x+a: a Є A} (i.e. the set obtained by adding x to every element of A. For example, if A = {1,2,3} then (1+ A) = {2, 3, 4}.) Show that sup(x+4)=x+ sup(A).