I would like to verify my work to make sure I did it correctly. Can someone plea
ID: 2941702 • Letter: I
Question
I would like to verify my work to make sure I did it correctly. Can someone please help me out??? Thanks :-)Q: For each of the following statements, formulate an English sentence that is its negation:
a) The set S contains at least two integers.
b) Mares eat oats and does eat oats.
c) I'm rough and I'm tough and I breathe fire.
d) This town is not big enough for the both of us.
e) I will marry Fred and disappoint Irving.
f) I cannot marry either Selma or Flo.
g) I will pay my taxes and avoid going to jail.
h) If I am a good boy then I will do fine.
i) I love everyone and everyone loves me.
j) If you study hard then you will do well in school.
k) If you get caught then you will go to jail.
l) If you work hard then you will succeed.
m) If you make more than $100,000 then you pay no income tax.
Explanation / Answer
Sounds like you're just asking for a check -- if you want an explanation for any of these just let me know. :)
a) The set S contains less than 2 integers.
b) Mares do not eat oats or does do not eat oats. (DeMorgan)
c) I'm not rough or I'm not tough or I don't breathe fire. (DeMorgan)
d) This town is big enough for the both of us.
e) If "marrying Fred" and "disappointing Irving" are separate things, then: "I will not marry Fred or I will not disappoint Irving." (DeMorgan)
Alternatively, this could be read as "I will marry Fred AND THEREFORE disappoint Irving," in which case the negation would be "I will marry Fred and not disappoint Irving." (Negation of a conditional statement: the hypothesis is true but the conclusion is false.) This is probably the better interpretation.
f) I can marry Selma or Flo.
g) Again, this could be read as separate: "I will pay my taxes (in my life) and I will avoid going to jail (in my life)," in which case the negation is "I will not pay my taxes or I will go to jail." Or it could be read as "I will pay my taxes in order to avoid going to jail," which is the conditional statement, "If I pay my taxes, then I will not go to jail," which negates as "I will pay my taxes and go to jail." (Hypothesis true, conclusion false.) The conditional statement reading is probably what they want.
h) I am a good boy and I will not do fine.
i) I do not love everyone or everyone doesn't love me. Equivalently, There is someone I do not love or there is somone who doesn't love me.
j) You study hard and you won't do well in school.
k) You get caught and you will not go to jail.
l) You work hard and you will not succeed.
m) You make more than $100,000 and you pay income tax.
Many of these have alternative ways of writing them, as well. If you have any questions or want further explanation on something, send me a message.