Symbolize and prove the following. Be sure to justify each step! \"Either scient
ID: 158642 • Letter: S
Question
Symbolize and prove the following. Be sure to justify each step! "Either scientists don't know what they are talking about, or the sun will eventually burn out and Earth will become dark and cold. If scientists don't know what they're talking about, then Mars is teeming with life. If Earth becomes dark and cold, then either the human race will migrate to other planets or will die out. Mars is not teeming with life, but the human race will not die out. Therefore, the human race will migrate to other planets."Explanation / Answer
Let us label the propositions.
S = scientist know what they are talking about
E = earth becomes dark and cold
M = Mars is teeming with life
H = human race will migrate
D = human race will die
1. Either scientists don’t know what they are talking about, or the sun will eventually burn out
and Earth will become dark and cold.
not(S) xor E
2. If scientists don’t know what they are talking about, then Mars is teeming with life.
not(S) => M
3. If Earth becomes dark and cold, then either the human race will migrate to other planets or will die out.
E => (H xor D)
4. Mars is not teeming with life, but the human race will not die out.
not(M) and not(D)
5. Therefore, the human race will migrate to other planets.
H
So the argument we want to show is:
1. not(S) xor E
2. not(S) => M
3. E => (H xor D)
4. not(M) and not(D)
-------------------
H
From 4, we can derive both:
* not(M)
* not(D)
From 2, since we have not(M), this reduces to not(S) => F.
Thus, not(S) has to be F for the statement to hold, which gives:
* S
From 1, we have (F xor E), so obviously, E must be T:
* E
Now we turn our attention to 3. Since we have E, we derive H xor D.
We have not(D), which means H:
* H
H = human race will migrate -------------------------proved
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