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neha goodgirl

Member

Registered: 2009-02-04

Posts: 2

Sets Problems

Problem 1:

{0} ≠ 0 , what does it mean? What does zero ( on right hand side) represent here?

Problem 2 :

Please tell me how to solve it:

The set S and E are defined as given below :

S : { (x,y) : |x-3| < 1 and |y-3| < 1}

E : { (x,y) :   4x^2 + 9y^2 - 32x - 54y + 109 ≤ 0}

Show that S is the proper subset of E.

I will be thankful for ur help.

Last edited by neha goodgirl (2009-02-04 23:39:35)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Sets Problems

{0} is a set containing 0 as an element, and 0 is just a number.
It's like on the left, 0 is in a box, but on the right it's on its own.

For the second one, you just need to prove that if some (x,y) satisfies the conditions on S, then it must also satisfy the condition on E.
You can do that by completing the square on E's equation.

Since you need to show that S is a proper subset of E, you also need to show that S isn't empty and S ≠ E.

ie. Find an (x,y) that satisfies the conditions on S, and find an (x,y) that satisfies E but not S.

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Why did the vector cross the road?
It wanted to be normal.