Final answer:
The statement 'The set of all polynomials with even coefficients' is false.
Step-by-step explanation:
The statement 'The set of all polynomials with even coefficients' is false.
A polynomial is a mathematical expression that contains variables and coefficients, combined using addition, subtraction, multiplication, and exponentiation. The coefficients are the constants in the expression.
An even number is a number that is divisible by 2 without leaving a remainder.
In this context, the statement is saying that all the coefficients of a polynomial are even numbers, which is not true. For example, the polynomial 3x^2 + 4x + 2 has coefficients that are not all even.