Sketch the graph of P and Q

**NeedHelp18** · September 16th 2008, 03:56 PM

P = x < 10/3
Q = -2 < or = x < or = 6

On a number line, sketch the graph of:

P:

Q:

P V Q:

P ^ Q:

(P V Q)':

I had this problem on a test, and i need to see if i got them right! thanks

oh and this one also:

state the negation of "3 + 2 = 5 or 10<2"

**Jhevon** · September 16th 2008, 06:07 PM

Originally Posted by NeedHelp18

P = x < 10/3
Q = -2 < or = x < or = 6

On a number line, sketch the graph of:

P:

Q:

P V Q:

P ^ Q:

(P V Q)':

it would be hard to draw these here

maybe Soroban can do it

I had this problem on a test, and i need to see if i got them right! thanks

oh and this one also:

state the negation of "3 + 2 = 5 or 10<2"

Let $P$ and $Q$ be statements. then,

$\neg (P \vee Q) = \neg P \wedge \neg Q$

now can you do it?

**Soroban** · September 16th 2008, 06:55 PM

Hello, NeedHelp18!

Don't stick in equal-signs so carelessly . . .

$P\!:\;\;x < \frac{10}{3}$

$Q\!:\;\;-2 \leq x \leq 6$

On a number line, sketch the graph of:

$(a)\;P$

. . . . $x < \frac{10}{3}$

. . $======o-----$
. . . . . . . . . . $^{\frac{10}{3}}$

$(b)\;Q$

. . . . $-2 \leq x \leq 6$

. . $--\bullet======\bullet--$
. . . . . $^{\text{-}2}\qquad\qquad\quad\; ^6$

$(c)\;P \vee Q$

. . . . $\left(x < \frac{10}{3}\right)\:\text{ or }\:(-2 \leq x \leq 6)\quad\Rightarrow\quad (x \leq 6)$

. . $=====\bullet--$
. . . . . . . . . $^6$

$(d)\;P \wedge Q$

. . . . $\left(x < \frac{10}{3}\right)\:\text{ and }\:(-2 \leq x \leq 6)\quad\Rightarrow\quad \left(-2 \leq x < \frac{10}{3}\right)$

. . $--\bullet====o--$
. . . . . $^{\text{-}2}\qquad\quad\;\; ^{\frac{10}{3}}$

$(e)\;(P \vee Q)'$