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

Mrs. avila is buying a wallpaper border to go on all of her kitchen walls. she wants to buy 5 extra feet of wallpaper border than she needs to be sure she has enough. she buys 55.5 feet of the border. the store owner selling the border uses the width of mrs. avila's kitchen to determine that the length of her kitchen must be 14.5 feet.

9.4.34  question   to estimate the height of a stone  figure, an observer holds a small square up to her eyes and walks backward from the figure. she stops when the bottom of the figure aligns with the bottom edge of the  square, and when the top of the figure aligns with the top edge of the square. her eye level is 1.811.81 m from the ground. she is 3.703.70 m from the figure. what is the height of the figure to the nearest hundredth of a  meter?

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?