Let a be a non-empty set and let s = p(a) be its power set. let b be a non-empty subset of a. on s, we define a relation r as r= {(a1, a2) esx sa, b = a, b} show that r is an equivalence relation. [2 marks] describe the equivalence classes of r when a = z and b = {1,2,3} [2 marks]

Ascale drawing of a lake has a scale of 1 cm to 80 m. if the actual width of the lake is 1000 m what is the width of the lake on the scale drawing

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe

Consider an example of a deck of 52 cards: example set of 52 playing cards: 13 of each suit clubs, diamonds, hearts, and spades ace 2 3 4 5 6 7 8 9 10 jack queen king clubs diamonds hearts spades what is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? assume that the cards are not replaced.