2. (a) Consider the statement \"if you don\'t like what you\'ve got, you should
ID: 3194874 • Letter: 2
Question
2. (a) Consider the statement "if you don't like what you've got, you should change it". Is it logically equivalent to "you like what you've got or you should change it"? What about to "if don't change what you 've got, then you like it"? And what about to "if you like what you've got, then you should not change it". Justify each answer. (b) A sign posted outside of Tokyo says "Here to attack the city? If so, you need to be green and at least 4m tall. If you are not green or at least 4m tall, then you can not attack the city. ". Write the two assertions on the sign in symbolic form using "a: you can attack the city", "g: you are green", and "t: you are at least 4m tall". Then determine whether they are logically equivalent. Can a green 1.65m tall dwarf monster attack the city? Choose one of the following and explain (i) no; (ii) yes; (iii) technically not, but go to town; good luck little dude!Explanation / Answer
Hi,
First step in such problems is to form the predicates and re write the statements given in terms of predicates using boolean logic like below
1. The two predicates would be
P- you like what you have got
Q- you should change it
now, the given statement is "If you dont like what you have got, you should change it" which translates to ¬P->Q
the other statement given is "you like what you have git or you should change it" i.e P Q
next statement is "if dont change what you've got then you like it" i.e ¬Q ->P
and lastly " if you like what you have got, then you should not change it" i.e P-> ¬Q
lets draw the truth table for each of these
So, if you see from truth table the propositions ¬P->Q , PQ and ¬Q ->P are equivalent but the other one is not.
b. Fortunately, the predicates are already given.
a- you can attack the city
g- you are green
t- you are atleast 4m tall
the given assertions are
"Here to attack the city? if so, you need to be green and at least 4m tall" which is equivalent to a-> gt
"if you are not green or at atleast 4m tall, then you cannot attack city" which is ¬g ¬t -> ¬a
we can again use the same truth table method now
hence they are equivalent
given height is 1.65 m i.e t is false
color is green i.e g is true
since ¬g ¬t is true means he cannot attack the city(from the second asserition)
Thumbs up if this was helpful, otherwise let me know in comments
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