SOLUTION: I dont get this logic stuff. Write a negation of the statement. Some athletes are musicians. would the answer be? some athletes are not musicians.

Question 482712: I dont get this logic stuff.
Write a negation of the statement.
Some athletes are musicians.
would the answer be? some athletes are not musicians.

Answer by tinbar(133) (Show Source): You can put this solution on YOUR website!
Logic is actually pretty easy if you just stay...logical.
Negation of a statement is the NOT version of the statement.
So let's symbolize this first so we can easily negate it using logic rules.
Statement: There exists x(A(x) AND M(x)) where A(x) means x is an athlete and M(x) means x is a musician
Technically the negation of this is: NOT(There exists x(A(x) AND M(x))). Using logic rules then we can move the negation inside one step at a time. First we have Not of There exists x (something about x), which is the same as For everything x Not(something about x) so in our first step we get For everything x, NOT ((A(x) AND M(x))). Using DeMorgan's laws we can simplify the second part, DM law's says that if you have NOT (A AND B), this is the same as (NOT A) OR (NOT B) so we get NOT ((A(x) AND M(x))) = NOT(A(x)) OR NOT(M(x))
And in total, we have For everything x (NOT(A(x)) OR NOT(M(x))) and if we translate it back we get: Everyone is either not a musician or not an athlete.
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