Sets true or false?

Question

Hello!

I have the following sentences:

1: ∅ ∈ {0}

2: {1} ∈ {1, {2, 3}}


3: 2 ∈ {1, {2, 3}}

4: 1 ∈ {R}

I know that the number 1 is true and all the others are false, but I can't understand why.

Thank you very much!

Answer 1

2 is false because 1 is an element but {1} is not an element and set {2,3} is an element 3 is false because 2 is not an element of the set but set {2,3} is an element 4 is false since the element is R and 1 is not R it is all because of the set brackets that makes 2 and 3 false. 4 is false because the set is R not the set of real numbers.