Need complete step-by-step explanation. Thanks :)

Need complete step-by-step explanation. Thanks :)

s", Carleton COMP1805 (Fall 2018] \"Discrete Structures 1" ' u N I v E n s I T Y Specication for Assignment 1 of 4 Your submission for this assignment must includeyourfull name (as it appears on cuLearn] and you nine-digit student number at the top of the first page. Yo ur submission must be a single pdf file with filename 'comp1805_f18_#########_a1.pdf (with the number signs replaced byyour nine-digit student number]. Your submission must have been created using Microsoft Word, Google Docs, or LaTeX. Submissions that are photographs or scans of handwritten submissions will not be accepted and will receive a mark of 0. Submissions that are compressed into an archive or submitted in the wrong format ( i.e., not "pdf'j will also be penalized and may receive a mark of 0. Do NOT compress your submissions into a "zip" archive. Late assignments will not be accepted and will receive a mark of 0. The due date for this assignment is Saturday, September 22, 2018, by 11:00pm. 1. Let p be the proposition "1 am a pig", q be the proposition "1 move quickly", and r be the proposition "1 am related to the wild boar". Translate the following expressions into English. [1.5 marks) a. rAq b. |T->Ip c. per 2. Translate the following English expressions into logical statements. You must explicitly state what the atomic propositions are (e.g., "Let p be proposition ...") and then Show their logical relation. [1.5 marks) a. It is a domestic pig but it is also kept as a pet. b. It is a guinea pig ifand only ifit is a rodent and it is born with its eyes open. c. [fit is a sea pig then it lives in the ocean and is actually a sea cucumber. 3. Determine which of the following are True and demonstrate why or why not by performing a reduction. [1.5 marks) a. 2 (.p V r ). For this question, you do not need to specify "how" you found the equivalent expression because you will show both techniques in questions 5 and 6 below. [0.5 marks] 5. Prove that the expression you found for question 4 above is equivalent to the expression q (.p V r ) by using only truth tables. Show all your work and do not skip any steps [i.e., ensure you that you include a new column for every single operation). [4.0 marks) 6. Prove that the expression you found for question 4 above is equivalent to the expression q (.p V r) by using only the logical equivalences. Show all your work and do not skip any steps. [4.0 marks] 7. Determine if the following expressions are tautologies, contradictions, or contingencies by using truth tables. Show all your work [10.0 marks) a. H? p c. ((p q) A (qVup)) /\\ (P A.q) d. . (((.r V .q) A q) A .p) 8. Let A[x] be the predicate "x is an alligator", B[x) be the predicate "x preys on the wild boar", C(x) be the predicate "x is a carnivore". Translate the following expressions into English, simplifying them as much as possible. The universe of discourse is all animals. [3.0 marks) a. Vx (806) 4) \"AUG V .A(x)) V C(30)) b. ax (C(x) /\\ .(A(x) v we)