Question

Consider the statement "There are no simple solutions to life’s problems." Write an informal negation for the statement, and then write the statement formally using quantifiers and variables.

Answer 1

Answer:

Step-by-step explanation:

To write the informal negation to the statement.

Let us first consider a statement and what the negation of a statement is defined as.

A statement is any sentence that can be determined as true or false. A statement can be written as P(x) or Q(x) .

For example, P(x) = 'a' likes rices.

Q(x) = b is a Maths student.

A negation to a statement is the opposite to that statement.

The negation of a statement P(x) is written as ~P(x).

If P(x) is "I am a boy", then ~P(x) (not P(x)) is "I am not a boy"

The negation of “There are no simple solutions to life’s problems” is “There are simple solutions to life’s problems.”

To write the statement formally using quantifiers.

MATHEMATICAL QUANTIFIERS:

1. For all, denotes as ∀

2. There exists, denoted as ∃

Let us define a Domain and a Set. A Set is simply a collection of objects.

Let X be the set of all simple solutions to all problems.

∀ x ∈ X, x is not a solution to life's problems.

Answer 2

solution is in the attachment