# convert statement to logical connectives

• Sep 21st 2008, 09:57 PM
zerodigit
convert statement to logical connectives
pls help me with this problem

let p ,q, r denote the following atomic statements

p:today is monday
q:the grass is wet
r: the dish ran away with the spoon

write the following in terms of p,q,r and logical connectives

1.Today is monday and the dish did not run away with the spoon

2.Either the grass is wet or today is monday.

3.Today is not monday and the grass is dry

4.The dish ran away with the spoon, but the grass is wet

By the way sorry for posting 2 threads consecutively.
• Sep 22nd 2008, 12:21 PM
Soroban
Hello, zerodigit!

Quote:

$\displaystyle p\!:\;\text{Today is Monday}$
$\displaystyle q\!:\;\text{The grass is wet}$
$\displaystyle r\!:\;\text{The dish ran away with the spoon}$

Write the following in terms of $\displaystyle p,q,r$ and logical connectives

$\displaystyle 1)\;\;\underbrace{\text{Today is Monday}}_{p}\; \underbrace{\text{and}}_{\wedge}\; \underbrace{\text{the dish did not run away with the spoon}}_{\sim r} \qquad p \;\wedge \sim r$

$\displaystyle 2)\;\text{Either }\underbrace{\text{the grass is wet}}_{q}\:\underbrace{\text{or}}_{\vee}\:\underbr ace{\text{today is Monday}}_{p} \qquad q \vee p$

$\displaystyle 3)\; \underbrace{\text{Today is not Monday}}_{\sim p}\:\underbrace{\text{and}}_{\wedge}\:\underbrace{ \text{the grass is dry}}_{\sim q} \qquad \sim p \;\wedge \sim q$

$\displaystyle 4)\; \underbrace{\text{The dish ran away with the spoon}}_{r}\: \underbrace{\text{but}}_{\wedge}\: \underbrace{\text{the grass is wet}}_{q} \qquad r \wedge q$