Answer the following questions: a) Prove the following logical truth (meaning the sentence can be proved without premisses), sometimes called the Drinker's Theorem: (∃x)(Dx → (∀y)Dy). b) After proving the theorem, reflect on what it is saying. c) Does it seem plausible that the Drinker's Theorem is a logical truth? d) What (if anything) makes the Drinker's Theorem seem strange?

Q: a) Calculate the following (First, you MUST show all the required formulas.) • Calculate P(R=F) =…

A: Provided that, R T F Total P(R) 0.01 0.99 1   A=T|R T F Total P(A=T|R) 0.9 0.1 1…

Q: Find the solution(s) in the set W for each of the following parts a) through h). a) 20 – x=x+6 O A.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 12) If CD = 15 and AB = 17 and CB = 6, fınd AD

A: Given,           In the diagram, CD is tangent to circles A nad B amd the circles are tangent to…

Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

A:

Q: |1 0 -3 8 7 45 0 1 a Let M(a, b) = where a and b are real numbers. a la 0 b 1| a) Evaluate M(a, b)…

A: Ma,b=10ab745-38b01aa0b1 Expanding the determinant along column 2, we get  Ma,b=10ab745-38b01aa0b1…

Q: Show that C@st-) is ving

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B)n (AUC)

A: To prove:- Prove that for any sets A, B, C we have AU (B∩C) = (AUB)  ∩(AUC) Method :- I use venn…

Q: (g) i–1 (h) i–2 (i) i -3

A:

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: (z + y)? 12. Prove: I = y if and only if ry Note, you will need to prove two 4 "directions" here:…

A: Case1: Prove, x=y if

Q: Prove that

A: Given parallel lines are l1=n→⋅x=c1..........1 And l2=n→⋅x=c2..........2. Let x1=OA¯ is a point on 1…

Q: 1. Translate these statements into English, where the do- main for each variable consists of all…

A: a) for all x, there exists y such that x is less than y b) for all x, for all y if (x is greater…

Q: State which of the following statements, are true, vacuously true, or false. (a) If A CAN B, then…

A: I have given the answer in the next step. Hope you understand that

Q: If |ū| = 4, |v|=5, |ū-v=6, determine |ū+ v.

A:

Q: Which of the following are always true, and which are not alwaystrue? Give reasons for your answers.…

A: Given statement is u×(v+w)=u×v+v×w

Q: の|=4+- COSU u =TX ノ H.W ノ

A: Given that  y=u+1/cosu  u=πx and x=1/4

Q: Given the two points (5, 28) and (7, 44): a) What is a third point that would make the relationship…

A:

Q: 6. Determine whether each of the following statements is true or false. If the statement is true,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

A:

Q: 2. ~P → (~Q AP) P F F F F

A: We can solve this using truth table

Q: DE congruent AE , BA || CE ,  CB ||  DA and m<C=65 . Find m<BAE

A:

Q: Prove both sides equal If T ≤p and π ≤v, then TUT ≤p Uv. τ υπ

A:

Q: Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. %3| Proof.…

A: the gcd of two integers is the largest positive integer that divides each of the integers.

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

A:

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: af 10x +11ly and = 11x. Which of the following is the best definition of (x,)) = If %3D Əx

A:

Q: (a) Show that point points i, 2i, 4i, 8i, 16i,... are equally spaced along the upper y-axis in the…

A: Given: Points: i, 2i, 4i, 8i, 16i, …….To show: a) Given points are equally spaced along with the…

Q: Construct a paragraph proof to prove the following: Given: y +2 = (x- 10) Prove: y =x-8

A:

Q: Prove the following arguments: E.g. &E, not simplification. 1.)   ∀x(Sx v Dx) ~Sa ∴∃xDx

A: Since you have asked for multiple question, we will solve the first question for you. If you want…

Q: 5. Solve for x. 5) s- A) 8 C) 10 -1+xX T k 2x+3 B) 2 D) -2 13 U 1 -V ➜

A: A detailed solution is given below.

Q: 3. If y x +2 and u = 2x -1 then %3D du a) x b) 1/x c) 2x d) x/2 e) None of the above answers

A: Given that y=x2+2 and u=2x-1To find dydu