Are the following statements?

Question

I started reading Logic. I am little confused whether the following are proposition or not.

1) Sum of two complex number is complex number

2)Sum of a real and a complex number will always be complex number,

3) If $x\in A \cup B$ , then $x \in B$

4) If $x\in A \cap B$ , then $x \in B$

my try----

1) This statement is true for all complex number. So the statement is true for any subset of complex number. So this is STATEMENT / PROPOSITION.

2) similar as (1). So STATEMENT.

3)This is not a STATEMENT.

4)This is true for any $A$ and $B$ so this is always true. No need to specify. This is a STATEMENT.

Can you please correct me if I go wrong anywhere?

Thank You.

Answer 1

2) is not a proposition because of 'would', that means that statement can not be only true or only false (not both) since it's ambiguous, you don't know what it's exactly saying, although it could work in some mathematical system in which 'would' is defined, say a statistics environment. 3) defines implicity $A$ and $B$ as sets, the fact that, in general is false just means that, but of course it's a proposition with the value 'false'.

Answer 2

I think you're mistaken about number $3.$ Just as in number $4,$ A and B are understood to be sets, and the usual interpretation of the statement in mathematics is that whatever sets A and B may be, the conclusion is true. This is not the case, so it a false statement.