Tutors help here

nj Create a truth table cominising (r - p) A(y + p) ad (rAg) + p. for alternatively tra required colmans as wooded. h) Using the table show, prove or disprove the following statement: (r -4 p) A (g - p) Problem 3. (Logic Panic) Three children (Mics, Bob, and Calling) are playing on the beard. An old man wells by and eats them, "After buding at both of your friends" foreheads, mis war And four or both of them have mud on Meir foreheads. " All worse children look at balk Mher friends and mise their heads. (Note in the butbeing problems, "they" is d s the grider-neutral procom appeared to the third person plural pronoun alLe A. B. C desole the proposition that Alice, Bob, and Cally have mod on their forchoads, respectively. Express the fact that all three children mained their hands in a Booken Gonzala wing A, B. C and appropriate logical operator(). byThe olf man then ands, "For s daller, withent toaching post cars forshred or looking in a merger or anything sender, tell the V yea here sat on your own Anchored wod how you know that " All three children are bouldered Why were all the children law ") After odd three children are bewildered in part b, one, my Alien, mince their hood and says, "I have mud on my forehead " Alice explains how they here this and roneions the dollar. What was Alice's logic? You MUST adequately explain your renaming to receive full credit. (1 Has without saying that that the old man is boncal, and the children are hood, able to make logic ming nal said the dollar.] problem, we explore the ishenut connection between Sudoku paralos and logie. Consider & 4 x Sucken pizzle repro m as blocks, Fier ear pouch, mom of the 16 colin, called gomoms, are andgood owa of the amadeus 1, 3, 3, 4, and the other polls are black. The pule is solead by signing a number to each black cell as thed ewer every column, and every one of the four 1 % 2 blocks contains each of the four pomible manbers. For each of the following questions, you MUST adequately explain your reasoning to receive bill THI. To simplify relation, ks VA texte I VP: V .. . VP. and denote por AGA...AN. You MUST express your anevers below using this condensed notations when ") To ascode a Sudolea posin, let pff j. of denote the proposition that is true when the sober is in is the cell in the ith now and jth cohnan. Foe sample, if the wuher i1 is given us the value in the find bow and first column, then we act p(1, 1, 3) to be trom, and bones p(l, 1, ) is tube for m / 1. In a ( x 4 Salka pauk, how many propositions pli. j, n) sat there for i, j,m - 1.23,4 b) We anart row i should contain the number n hu any boost im 1,2,1,4 mal Axed a - 1,1,3, 4 - Expres this information using the progueltion pll J, n) and the appropriate bockca Solution. The solthe by this part is given to you. For a fixed now & and first number s. could be in the ed in row i edas j kir j - 1,3,1,we )Express the sertion that a fived row d contains all manberan for n - 1,2, 3,4 using the proposition pli j. a) and the appropriate brind epastors). (list: take advantage of your solution in (bj.] Solution. The solution for this part is gives to you, Can you figure out why? d) Express the mention that eury nas'f contains easy mather s be i,n - 1.2,84 using the proposition p(. J.n) mad the appropriate logical operators), Explain your reviewing Hint: take advantage of youa solution in (c).) istion that every column j contains cyory number a fu j,= = 1,2, 3, 4 ning, the proposition p(i, An) and the appropriate logical operator(=). {)Express the amertion that each of the fair 2 x 2 blocks contain every number n hu - 1, 2, a, 4 wing the proposition pli, J, n) and the appropriate logical operatorja). (Hint: draw 4 x 4 grid and determine how to hucke cack 2 x 2 adgrid)