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See the answer Show transcribed image text Expert Answer 100% (1 rating)Head Office 127, Zone II, MP Nagar, Bhopal Page 13 of 16 Hence, A's mother is D's sister The Teacher is married to the Musician From (6), we get Engineer and Accountant are in the second generation Engineer is the husband of Lawyer and Accountant is the wife of Doctor From (5), we get C, E and G are of same gender which means that C, E and C are females as E isEx 91, 5 The points P, Q, R, S, T, U, nd B on the number line are such that, TR = RS = SU and AP = PQ = QB Name the rational numbers represented by P, Q, R and S
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Q ≠ Q ×And the conclusion is~~s→q We then create truth tables for both premises and for the conclusion Again, since our argument contains four letters p, q, r, and s, all of our truth tables should contain both all four of these letters and shouldTransposition (p → q) ∴ (¬q → ¬p) if p then q is equiv to if not q then not p Material Implication (p → q) ∴ (¬p∨q) if p then q is equiv to not p or q Exportation ((p∧q) → r) ∴ (p → (q → r)) from (if p and q are true then r is true) we can prove (if q is true then r is true, if p is true) Importation (p → (q
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Transcript Example 2 If P = {a, b, c} and Q = {r}, find the sets P ×P then q" or "p implies q", represented "p → q" is called a conditional proposition For instance "if John is from Chicago then John is from Illinois" The proposition p is called hypothesis or antecedent, and the proposition q is the conclusion or consequent Note that p → q is true always except when p is true and q is falseBecause of the nature of the &
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P = { (a, r), (b, r), (r, a), (r, b), Since (a, r) ≠ (r, a) P ×(p →q)∧(q →r)∧p ⇒r We can use either of the following approaches Truth Table A chain of logical implications Note that if A⇒B andB⇒C then A⇒C MSU/CSE 260 Fall 09 10 Does (p →q)∧(q →r)∧p⇒r ?How to prove ¬(P ∧ ¬Q), ¬P → Q ∴ Q using Fitchstyle natural deduction system?
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Q = {a, b, c} ×Result 25 (Elimination) Suppose p and q are statement forms Then the following arguments (called elimination) are valid p∨q ∼ p q p∨ q ∼ q p Result 26 (Transitivity) Suppose p, q and r are statement forms Then the following argument (called transitivity) is valid p → q q → r p(pVq) V (~p^q) → q p q ~p p V q ~p ^ q (p V q) V (~p ^ q) (p V q) V (~p ^ q) → q T T F T F T T T F F T F T F F T T T T T T F F T F F F T Problem 18 (15 points) Write each of the following three statements in the symbolic form and determine which pairs are logically equivalent a
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P = {a, b, c} and Q = {r} P ×If P is the husband of Q and R is the mother of S and Q, what is R to P ?P, the whitecolored house, is taller than R, but shorter than S and Q The heights of P, Q, R, and S can be arranged in two ways One of the ways is {S, Q, P, R} and another way is {Q, S, P, R} Therefore, {P, U, S} are one side on the road, and {R, Q, T} are on another side of the road P is opposite to R, U is opposite to Q and S is opposite
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Example 232 Show (p!q) is equivalent to p^q Solution 1 Build a truth table containing each of the statements p q q p!q (p!q) p^q T T F T F F T F T F T T F T F T F F F F T T F F Since the truth values for (p!q) and p^qare exactly the same for all possible combinations of truth values of pand q, the two propositions are equivalentExplore posts in the same categories Uncategorized This entry was posted on at 9 am and is filed under UncategorizedYou can subscribe via RSS feed to this post's comments s communicating with doctors You can comment below, or link to this permanent URL from your own siteConsider, for example, Implication Elimination, shown below on the left If we have (p ⇒ q) and we have p, then we can deduce q The clausal form of the premises and conclusion are shown below on the right The implication (p ⇒ q) corresponds to the clause {¬p, q}, and p corresponds to the singleton clause {p}
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