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How can this English sentence be translated into a logical expression ?
“You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”

3 Answers

Best answer
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P=you can ride the roller coaster

Q=you are under 4 feet tall.

R=You are older than 16 years old

use of if : A if B $\equiv B \rightarrow A$

use of unless : A unless B $\equiv \bar{B} \rightarrow A \equiv ~~B \vee A$

now,

$\bar{Q} \rightarrow \bar{P}$ unless $R$

$\equiv Q \vee \bar{P} \vee R$

$\equiv Q \vee R \vee \bar{P}$

$\equiv$  not $(Q \wedge \bar{R})  \vee \bar{P}$

$\equiv (Q \wedge \bar{R}) \rightarrow \bar{P}$

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3 votes
3 votes
P=you can ride the roller coaster

Q=you are under 4 feet tall.

R=You are older than 16 years old

keynote:Here unless will negate R

Q^~R-->~P

See the example in Rosen for more explanation.
1 votes
1 votes
p=you can ride the roller coaster
q=you are under 4 feet tall
r=you are older than 16 years
                                                           now see in question question said you can not ride the roller coaster i.e (p')
we can written like that -
you are under 4 feet tall "and" you are not older than 16 years old both statements are same
now simple-
p--> q i.e( q if p ) right .....means before if always came conclusion so in above question before if is statement "p" i.e p will be conclusion i.e p'
now,     q
q^r'  -->p'

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