Use the Laws of Algebra of sets and Logic to prove that: (i)P  Q is logically equivalent to ( P  Q) ? [1 mark] (ii)Find the negations of P  Q ? [3 marks] (iii)Using Truth Table that: P  Q  (P  Q)  (Q  P) ? [2 marks] b) Determine the duality of the Boolean equations (i) (a . 1)  (0  a)  0 [1 mark] (ii) a . (a  b)  a . b

Write an equation in point-slope form for the line through the given point that has the given slope (-2,-7); m=-3/2

See attachment below and find the equivalent of tan(∠qsr)

Asample of 200 rom computer chips was selected on each of 30 consecutive days, and the number of nonconforming chips on each day was as follows: the data has been given so that it can be copied into r as a vector. non.conforming = c(10, 15, 21, 19, 34, 16, 5, 24, 8, 21, 32, 14, 14, 19, 18, 20, 12, 23, 10, 19, 20, 18, 13, 26, 33, 14, 12, 21, 12, 27) #construct a p chart by using the following code. you will need to enter your values for pbar, lcl and ucl. pbar = lcl = ucl = plot(non.conforming/200, ylim = c(0,.5)) abline(h = pbar, lty = 2) abline(h = lcl, lty = 3) abline(h = ucl, lty = 3)