Answer: a. Yes
b. No
a. Yes, the set of linear binomials has closure for addition. Closure means that when we add two elements from the set, the result is also an element of the set. If we add two linear binomials, ax + b, and cx + d, we get (a + c)x + (b + d), which is still a linear binomial.
For example, if we have the linear binomials 2x + 3 and 4x + 1 when we add them together, we get (2 + 4)x + (3 + 1) = 6x + 4, which is still a linear binomial.
So, the set of linear binomials has closure for addition.
b. No, the set of linear binomials does not have closure for subtraction. Closure means that when we subtract two elements from the set, the result is still an element of the set.
For example, if we have the linear binomials 2x + 3 and 4x + 1 when we subtract the second one from the first, we get (2x + 3) - (4x + 1) = -2x + 2, which is not a linear binomial.
The result of the subtraction is a linear monomial, not a linear binomial. Therefore, the set of linear binomials does not have closure for subtraction.