[for real number y, y*y=-1] is this statement or open statement?
no. in fact, there is no value of y which makes it true.
you are saying it's not open statement or what I don't really understand what you just saying
To determine whether the statement "[for real number y, y*y=-1]" is a statement or an open statement, we need to understand the definitions of these terms.
A statement, in the context of logic and mathematics, is a complete sentence that can be considered either true or false. It is an assertion or a proposition that can be evaluated to either be correct or incorrect.
On the other hand, an open statement is a sentence that contains one or more variables and becomes a statement when specific values are assigned to these variables. Open statements are neither true nor false until the variables are given specific values.
In the given statement, "[for real number y, y*y=-1]", the variable 'y' represents a real number. This sentence can be considered an open statement because it contains a variable that can take different values and does not provide any specific value for 'y'. The statement becomes a complete statement when you give a specific value to 'y', which makes it either true or false.
For example, if we substitute 'y' with the value -1, the statement will be "(-1)*(-1) = -1", which is a true statement since the square of -1 is equal to 1, not -1.
Therefore, "[for real number y, y*y=-1]" is an open statement.