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True/false units,amounts of plane figures

Petrus

Well-known member
Feb 21, 2013
739
Consider the following amounts of plane figures: A = {All squares}, B = {all diamonds}, C = {all rectangles}, D = {all parallelograms}, E = {all trapezoidal with three equal sides}, F = {all trapezoidal with at least a straight corner angle}. Examine which of the following statements are true. Reply with the letter R (true) or F (false).
__________ (a) B U C= D
__________ (b) D ∩ F= C
__________ (c) D ∩ E= B
_________ (d) F "subset" D U E
__________ (e) E ∩ F= B ∩ C

Any advice?
 
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soroban

Well-known member
Feb 2, 2012
409
Hello, Petrus!

Examine which of the following statements are true.
Reply with the letter T (true) or F (false).

__________ (a)
__________ (b)
__________ (c)
__________ (d)
__________ (e)


Any advice?

Yes . . . Give us the statements!
 

Petrus

Well-known member
Feb 21, 2013
739

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Can you begin by stating the definitions of the various plane figures given?
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
For example, with reference to (a), is it true that all diamonds and all rectangles are parallelograms? Or are the any parallelograms that are NOT diamond or rectangles? To answer that, obviously, you need to know the definitions of "diamond", "rectangle", and "parallelograms".
 

Nehushtan

New member
Mar 11, 2013
5
Re: Plane figures

By “diamonds” you mean rhombuses, right?
 

Petrus

Well-known member
Feb 21, 2013
739
Can you begin by stating the definitions of the various plane figures given?
Romb:eek:ppisite side paralell and its quadrilateral.
Rectangle: its quadrilateral and its 90 degree on corner.
Paralellograms: is a romb,square and rectangle. Quadrilateral
Trapezoid: quadraliteral, paralellograms,rectangle, romb, square ( its a isoceles trapezoid)
square: quadraliteral , same lengt all side, 90 degree, specialfall romb rectangle paralellograms,trapezoid

- - - Updated - - -

By “diamonds” you mean rhombuses, right?
Yes
 
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Petrus

Well-known member
Feb 21, 2013
739
Can someone try explain for me what i am doing wrong, i get (a) is correct i get (b) is false cause e dont got parallel sides, (c) is false cause e is none parallel sides, (D) is correct and (e) is false cause e is none parallel
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
Consider the following amounts of plane figures: A = {All squares}, B = {all diamonds}, C = {all rectangles}, D = {all parallelograms}, E = {all trapezoidal with three equal sides}, F = {all trapezoidal with at least a straight corner angle}. Examine which of the following statements are true. Reply with the letter R (true) or F (false).
__________ (a) B U C= D
__________ (b) D ∩ F= C
__________ (c) D ∩ E= B
_________ (d) F "subset" D U E
__________ (e) E ∩ F= B ∩ C

Any advice?
Can someone try explain for me what i am doing wrong, i get (a) is correct i get (b) is false cause e dont got parallel sides, (c) is false cause e is none parallel sides, (D) is correct and (e) is false cause e is none parallel
Hi Petrus! :)

Let's see, your sets look visually like:
Code:
A
\begin{tikzpicture}
\draw (0,0) rectangle (1,1);
\end{tikzpicture}

B
\begin{tikzpicture}
\draw (0,0)-- (1,0) -- (1.707,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}

C
\begin{tikzpicture}
\draw (0,0) rectangle (3,1);
\end{tikzpicture}

D
\begin{tikzpicture}
\draw (0,0)-- (3,0) -- (4,1) -- (1,1) -- (0,0);
\end{tikzpicture}

E
\begin{tikzpicture}
\draw (0,0)-- (2.414,0) -- (1.707,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}

F
\begin{tikzpicture}
\draw (0,0)-- (3,0) -- (3,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}
Oh sorry, tikzpictures do not work yet.
(Just practicing, just in case they will work someday. ;))

geometric_figures.png

Let's start with (a) B U C= D.
So those are the diamonds (B) together with the rectangles (C).
And the question is whether that matches with the parallelograms (D).

Well, a diamond is a parallelogram, so that's okay.
A rectangle is a parellelogram, so that's okay too.
But... a generic parallelogram is neither a diamond nor a rectangle.

So no, (a) is not correct. It is false.
 

Attachments

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Nehushtan

New member
Mar 11, 2013
5