Question

Which of the following sets are closed under addition?

(i) The set of all vectors in R^2 of the form (a, b) where b.
A) {All real numbers}
B) {All vectors in R^2}
C) {All even numbers}
D) {All odd numbers}

Answer 1

The set that is closed under addition is the set of all vectors in R^2 of the form (a, b) where b.

Step-by-step explanation:

The set that is closed under addition is the set of all vectors in R^2 of the form (a, b) where b.

To determine if a set is closed under addition, we need to check if the sum of any two vectors in the set is also in the set.

In this case, if we add two vectors (a, b) and (c, d) from the set, we get (a+c, b+d). Since a, b, c, and d are real numbers, the sum (a+c, b+d) is also a vector of the same form, which means it is still in the set. Therefore, the set of all vectors in R^2 of the form (a, b) is closed under addition.