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Expert: - 2/18/2011


Question
B is equal to
Bracket (x,y) is an element of real numbers*2:y is greater than or equal to 2x + 1 bracket

C is equal to
Bracket (x,y) is an element of real numbers*2:y is greater than or equal to (x+1)*2 bracket

Show that C is a proper subset of B.

Thank you.

Answer

Inequality
Questioner: ancy
Country: United Kingdom
Category: Advanced Math
Private: Yes   <<<<<<<<<<<<<< Changed.
Subject: subsets
Question:

B = { (x,y) in RR : y >= 2x + 1 }

C = { (x,y) in RR : y >= (x+1)*2 }

Show that C is a proper subset of B.

Do you have a definition of 'proper subset of'?  Most stuff will yield easily to applying the definition correctly.

C < B means:

I. (x,y) in C => (x,y) in B

and

II. There exists (x,y) in B which is not in C.

I would suggest that simple graphs of B and C will give you the clue.

For I, you might want to show:

for all x, (x + 1)^2 >= 2x + 1

For II, refer to the graph for your examples.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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