1. Translate each of the following sentences into symbolic logic, then find their negation. (a) Everyone who is majoring in math has a friend who needs help with their homework. (b) Everyone likes someone, but no one likes everyone. (c) There exists a non-zero real number a such that a+ x = x, for every real number x. (d) Every non-constant polynomial p(x) is such that its derivative is not zero. (e) For every positive number M, there exists a positive number N such that f(x) > M whenever x > N.
1. Translate each of the following sentences into symbolic logic, then find their negation.
(a) Everyone who is majoring in math has a friend who needs help with their homework.
(b) Everyone likes someone, but no one likes everyone.
(c) There exists a non-zero real number a such that a+ x = x, for every real number x.
(d) Every non-constant polynomial p(x) is such that its derivative is not zero.
(e) For every positive number M, there exists a positive number N such that f(x) > M whenever x > N.
(a) x is a person
p(x) = x is majoring in math
q(x) = friend who needs help with their homework
The given statement is
Negation of this statement would be .
That is,
There is a person who is majoring in math and has a friend who doesn't need help with their homework.
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