Algebra

Please help me with the attached algebra problems.

Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider X\E = Y. Show that all sets B which can be expressed as A\E, where A belongs to the sigma algebra in X, form a sigma-algebra in Y. Please justify every step and claim you make in the solution.

1. Very rarely do people use algebra in their jobs or their lives. At most, people use arithmetic. If this is the case then why do you suppose it is that we study algebra in the first place?

3x-2(a-3)=4x-b-a -3/4t =1/2

Please see attachment. Thank you very much!

11b. A boolean algebra can be made into a partially ordered set by letting a≤b mean a=b. Show that a≤b iff b= a + b

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only 'food for thought.' I welcome your constructive ideas and comments on one or several of them. Whether you agree or do not agree, the study of algebra is good for the brain. The b

See Attached for algebra equation

Modern Algebra Set Theory (XVIII) Laws of Algebra of Sets

The drying time of varnish depends on the amount of certain chemical that s added. a. Determine a best (least-squares) ft parabola of the form: T(m) = x1 + x2m + x3m^2 to the data provided n the table below b) Also, estimate the drying time of the varnish when 3.5 grams of the chemical are added. Mass (m) of Additive (Gr