Thread: Sketch the graph of P and Q

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"

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 $\displaystyle P$ and $\displaystyle Q$ be statements. then,

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

now can you do it?

Hello, NeedHelp18!

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

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

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

On a number line, sketch the graph of:

$\displaystyle (a)\;P$

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


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

$\displaystyle (b)\;Q$

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


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

$\displaystyle (c)\;P \vee Q$

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


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

$\displaystyle (d)\;P \wedge Q$

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


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

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

. . . . $\displaystyle (x \leq 6)'\quad\Rightarrow\quad (x > 6)$


. . $\displaystyle ---o====$
. . . . . . .$\displaystyle ^6$

State the negation of: .(3 + 2 = 5) or (10 < 2)

. . $\displaystyle \text{(3 + 2}\neq 5)\:\text{ and }\:(10 \geq 2) $