Question

Write the following as English sentences. Say whether they are true or false. 1. ∀x∈x,x 2=0 6. ∃n∈N,∀X∈P(N),∣X∣p. 4. There exists a real number a for which a+x=x for every real number x.

Answer 1

Three mathematical statements are provided, and their truth value is determined and corrected if necessary.

Step-by-step explanation:

The given statements are:

1. ∀x∈x,x²=0
2. ∃n∈N,∀X∈P(N),∣X∣p
3. ∃a∈ℝ,(a+x)=x ∀x∈ℝ

1. The statement '∀x∈x,x²=0' is false. The correct statement would be '∀x∈x,x³=0'.

2. The statement '∃n∈N,∀X∈P(N),∣X∣p' is false. The correct statement would be '∃n∈N,∣X∣=0 ∀X∈P(N)'.

3. The statement '∃a∈ℝ,(a+x)=x ∀x∈ℝ' is true. It is true because for any real number x, if we choose a=0, the equation (a+x)=x becomes (0+x)=x which simplifies to x=x which is always true.