- #1
nirajnishad
- 16
- 0
Homework Statement
X={4^n-3n-1/ n belongs to N}
Y={9(n-1)/ n belongs to N }
Homework Equations
then,
XUY is equals to X or Y or N or None of these
A polynomial being an element of N means that its coefficients and variables are all natural numbers (positive integers). In other words, the polynomial only contains non-negative powers of the variable, and all coefficients are non-negative integers.
X and Y can be any type of polynomial as long as their coefficients and variables are all natural numbers. This means they can be monomials, binomials, trinomials, or any other type of polynomial as long as they meet the criteria of being an element of N.
This statement specifies that n is an element of N, meaning that n must be a natural number. Without this specification, n could potentially be any real number. Additionally, stating that n is an element of N also implies that the coefficients and variables of X and Y must also be natural numbers.
Polynomials of n have all the same properties and rules as any other polynomial, as long as they meet the criteria of being an element of N. This means they can be added, subtracted, multiplied, and divided (except by 0) just like any other polynomial.
Yes, the statement can be rewritten in this way. It is essentially saying the same thing, just in a different order. However, the original statement is more commonly used and may be easier to understand for some individuals.