Please show all steps of your work on the text box below (wo…

Please show all steps of your work on the text box below (work shown on the scratch paper is NOT graded). Consider the following sets.  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}P = {1, 2, 4, 7, 8}Q = {2, 3, 5, 8, 10}R = {1, 3, 4, 6, 8} (P U Q) ∩ R P’ ∩ R What regions (e.g. 1, 4, 8) of the following Venn diagram would be shaded for (P U Q) ∩ R?

Please show all steps of your work on the text box below (wo…

Please show all steps of your work on the text box below (work shown on the scratch paper is NOT graded). Use the ceiling and floor function to determine the following values:a) There are y passengers waiting to board a train. The train can hold up to 88 passengers per trip. How many trips are required to transport all the passengers? b) Jason has x pens and wants to give 4 pens to each friend. How many friend will receive the full number of pens?

Please show all steps of your work on the text box below (wo…

Please show all steps of your work on the text box below (work shown on the scratch paper is NOT graded). Consider three functions f, g, and h, whose domain and target are Z. Let f(x) = x3 – 1, g(x)= 3x + 2, h(x)= |x – 3|. Evaluate the following.  a. Evaluate (f ο h) (27) b. Evaluate (g ο h ο f) (10) c. Give a mathematical expression for (h ο g o f)