Given: If X, then not Y. If not Y, then Z. Y is true. So: (A) X is false, Z is unknown B) X is true, Z is true X is unknown, Z is unknown X is unknown, Z is true

Q: Give direct and indirect proofs of: p→q,¬r→¬q,¬r⇒¬p. p→¬q, ¬r→q, p⇒r. a∨b, c∧d, a→¬c⇒b.

A: Direct proof :  step  reason 1. p→q premise  2.¬p→¬q premise  3. ¬r premise  4. ¬q 2,3,MP…

Q: Say whether the following are correct. If yes, provide a natural deduction proof. If not, provide a…

A: For (c), We are given the following expression.     Q∨P, ¬Q→R, P∨R⊦Q→P That is, we need to verify…

Q: Given: p and r are True; q and s are False 1. pV-qV-r. 2. (q V - p)= -r. 3. qArA-s. _

A: we have been given that p and r are True and also q and s are False  first, we will find the answer…

Q: W 5.) Y Given: 00 ZSWO = ZTVO ZWSO = ZVTO Prove: ASWO ΔTVΟ Statements Reasons

A:

Q: Given the statement p and q such that p: John is tall; q: John is fat. The statement - pA ~q is…

A: Give the statements  P : John is tall q : John is fat  To find :-  The equivalent statement to ~p^~q

Q: Suppose that (r ^ q) V (p → r) is known to be false. In this case, which of the following statement:…

A: Solution: Given r∧q∨p→¬r is false. Since p→¬r≡¬p∨¬r Therefore, r∧q∨¬p∨¬r is false We know that if…

Q: One of the following statements is False. Is it a, b, c, or d?

A:

Q: which of the following statements are true? S

A:

Q: 2. Make the following assumptions and find the truth value of the given compounds. A is true, B is…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: Given: If A, then B, and vice-versa. What can be deduced from the facts below? Fact: A is true. So B…

A: We can use the truth table to find the answer.

Q: Suppose p is true, q is true, r is true, s is false. Then (-p v s) v (q ar) O True O False

A:

Q: Suppose you have the following premises: Sr What is a relevant conclusion that can be drawn? Select…

A: Given the following premises:       p∧qp→¬q∧rs→r Find the relevant conclusion.

Q: Given: If X, then not Y. If not Y, then Z. Y is true. So: 1) x is true, z is true 2) x is unknown,…

A: Given that X→¬Y                  (1) ¬Y→Z                  (2) Since if X, then not Y does not…

Q: Let R={y,p}, S={z,p,u}, and T={r,y,p,u,z}, For each of the following questions, enter T if the…

A: Given that R={y,p} ,S={z,p,u} ,and T={r,y,p,u,z}1) R has the element y, but S does not have y in it.…

Q: (b) Consider the statement: if x 0, then r< y. State the hypothesis P(x,y) and the conclusion Q(x,…

A: Consider the statement " If x≤y+∈, ∀∈&gt;0, then x≤y."

Q: Disprove by Contradiction If a,b,c ∈ ℕ, then at least one of a-b, a+c and b-c is even.

A:

Q: Use the Law of Negative Inference to draw a valid conclusion for this argument. 1. If the weather is…

A: Law of Negative Inference P → Q       -Q       C.  ∴ - P

Q: Note that “a sufficient condition for s is r” means r is a sufficient condition for s and that “a…

A: The given statement is “A sufficient condition for Jon’s team to win the championship is that it win…

Q: Which statement below is true? A. If p q is true, then q p is true. > B. If p q is true and p is…

A: We have to state which is true from the given option.

Q: Given: < 2 S <3 Prove: < 1 and < 3 are supplementary Statement Reason Given

A: Given query is to prove that angle 1 and 3 are supplimentary.

Q: In the question as follows, determine whether the statement is true or false. If it is false,…

A: A sequence is a function from the set of natural numbers to the set of real numbers. For a sequence…

Q: Suppose that p is false, but q is true. Which of the following statements are also true? Select all…

A: Given the statement p is false, but q is true.

Q: If Ac B and A c D, then B c D. True False

A:

Q: Given: If X, then not Y. If not Y, then Z. Y is true. So:

A:

Q: Suppose L(x) = "x is a llama" and E(x) = "x is an emperor." Do the following to statements mean the…

A: Consider the given information:

Q: For the given facts, indicate what can be deduced from the if-then statement whose reverse is also…

A: The given statement is "If Jackie is under 14, then Kim is under 12" It's reverse is correct. And…

Q: Verify that the following statements are tautologies. 1) Transitive Law [(p → q)A(q → r)] → (p → r)…

A: 1)Transitive law[(p→q)∧(q→r)]→(p→r)2)Law of Excluded Middle p∨~p3)Law of Syllogism[p∧(p→q)]→q

Q: If p, q and r are all TRUE statements, which of the following is FALSE? ~ (р^q) —т a. O b. ~pHN (q V…

A:

Q: ii- Given the following Premises: ¬A → (CAD) A → B ¬B Prove: C.

A:

Q: Which of the following is equivalent to (p^ (p → q)) → q? a) True b) False c) Contradiction b and c

A: Let's find.

Q: If vy 3x P(x, y) is true, then 3x Vy P(x, y) is also true O Yes O No

A:

Q: Given : if x, then Y. If Y, then Z. Y is true, So:

A: Given : if x, then Y. If Y, then Z.

Q: If X, then Y. If Y, then Z, y is true, So:

A:

Q: If X, then not Y. If not Y, then Z. Y is true. So: X is unknown, Z is unknown  X is unknown, Z is…

A:

Q: Given: If X, then Y. If Y, then Z. Y is true. So:   a) x is unknown, z is unknown b) x is…

A:

Q: Given that a is false and b is false. Which of the following is FALSE? Oa + b Oa - b Oavb O-a A-b

A: Given: a is false and b is false. To find: Which of the given is false.

Q: 9. If PIg 9 ||r ||s. and sl then which of the following statements is not true?

A:

Q: Given: If X, then Y. If Y, then Z. Y is true. So: X is unknown, Z is unknown X is unknown, Z is true…

A: It is given that “If X, then Y. If Y, then Z”. From the given statement it is clear that, If X, then…

Q: If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR y') AND (x' AND y')') OR ((w OR y')' AND (x…

A: If w is FALSE, x is TRUE, and y is FALSE, we need to find ((w OR y') AND (x' AND y')') OR ((w OR…

Q: If the statement is p∨qp∨q is false , and pp is false , then q must be ____ ? Select one: True…

A: given that                                     is FALSE. Now truth table for this will be p q…

Q: Which of the following statements is false? O Vr e REnE Z:r·n E Z O vq e Q3n E Z: 4 € Q O 341 E Q\…

A: Real analysis problem......

Q: 4. Given: BC + BE = AD, BE = EF Reason: Conclusion: BC + EF = AD

A:

Q: 5. Mandy has the two triangular pieces of cloth pictured below. M If AL MN = A PRQ, which statement…

A:

Q: Say we are given that the statement p^ (p → q) is true. Can we deduce the statement q?

A: By using rules of inference on the given statement we deduce the conclusion q.

Q: If vy 3x P(x, y) is true, then 3x vy P(x, y) is also true O Yes O No

A: Given statement is If ∀y ∃x P(x,y) is true, then ∃x ∀y P(x,y) is also true.

Q: In the diagram, MN/MR=MP/MQ. Which of the statements must be true? 1. ΔMNP~ ΔMRQ 2. ∠ 1 ≅ ∠2 3. ∠1 ≅…

A: Here we discuss triangle property

Q: When does vxayP(x, y) be true? A) P(x, y) is true for every pair x, y. В For every x there is a y…

A: Given that, ∀x∃y P(x,y)

Q: are proving tregnes # 4 Statementa Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5.

A:

Q: 7.) V W TV = XW VA = WA ΤΑΧΑ Given: Prove: ATVA = AXWA Statements Reasons

A: We will prove this by checking the postulates of triangle triangles as shown below we know that If…