Exercises. Prove the following: 1. A ∧ (B ∧ C) ⊢ C 2. A ∧ (B → C), A → B ⊢ C 3. A ∧ (B ∧ C) ⊢ (A ∧ B) ∧ C 4. A, A → B ⊢ A ∧ B 5. A ∧ B, B → C ⊢ A ∧ (B ∧ C) 6. A → B ∧ C, A ∧ D ⊢ B ∧ C 7. A → C ⊢ A ∧ B → C ∧ B 8. A ∧ B → C ⊢ A → (B → C

Q: (avb)л (aVc) d → e (bA c) → (F → k) ^ c) .. -F

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Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: -8 -2 -9 6 4 4 0 4 w is in Col A. Is w in Nul A? Let A = 8 and w= 27 -2 Determine if

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Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

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Q: Let A, B, and C are three sets, prove that Cx (A – B) = (C x A) – (C × B) C.

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Q: given A={x I x2 - 1 = 0 }, B = {x I x2 + x - 2 = 0}, and C = {x I x3-x2=0} A, B, C Ⅽ R a. A U ( B ∩…

A: A=x:x2-1=0B=x:x2+x-2=0C=x:x3-x2=0 Then we have to evaluate A∪B∩C.

Q: Let U, A, and B be defined as shown below. U ={a, b, c, d, e, f, g, h, i, j } A = { c, d, e, g, i} B…

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Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: B D a Set A e (AUB) U{d}=A (A/B) n (B/A) = {} (B/A) U{a,b,c} = B A\(ANB) = {e,f} e Set B to d

A: Explaination of the answer is as follows

Q: Y={a,b,c,d,f} Is the following statement True? ∅⊆Y

A: The given set is                        Y={ a , b , c , d , f } We know that for every set S , S⊂S ,…

Q: 2. Let U= {x:x E Z ,0<x< 10} , A= { x:x € N ,x² – 5x = -6}, B ={ a , b} and C={c, d, e }: ( Hint: a…

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Q: Determine whether each of the following  statements are True or False and why:…

A: 1) False. A set A is a subset of a set B if and only if every element in A is in B.For any sets A…

Q: 5. Аx (В — С) %3D (А х В) — (А хС) 6. (А - В) хС %3 (АxC) — (В хС)

A: To prove the given statements.

Q: Check that P ˅(Q ˅ R) is equal to ┐(R ˄ Q ˄ P) → P

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Q: true or false: 1. Q+ ∩ R+ = R+ 2. Z+ ⊆ R+ 3. C U R = R 4. Q ∩ Z+ ⊆ R+ please explain for each…

A: We have to answer that which statement is true and which one is false with reason.

Q: Let \(U={a,b,c,d,e,f,g,h}, A={a,b,c,d}, B={b,e,a,d}, C={e,a}\}. Identify if the following statement…

A: The size of a set is defined as the number of distinct elements of that set. This is also called the…

Q: True or False?

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Q: X X P(X=x) 0,10 0,20 0,30 0,40 2 3 4 5 P(2<X<4)=??? O A) 0,20 B) 0,10 C) 0,40 D) 0,50 O E) 0,30

A: Given observations

Q: 2. ~P → (~Q AP) P F F F F

A: We can solve this using truth table

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: Let u = (2, -2, 3), v = (1, -3, 4), and w=(3, 6, -4). Evaluate the following 1. ||3u-5v+w||…

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Q: If A is a subset of B, and B is a subset of A, then does A=B?(Y/N) If A maps onto B, and if B maps…

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Q: Find P(C1)  l. Find P(V4)  m. Find P(C1 ∩∩ V4)

A: As per guidelines we are allowed to solve maximum of 3 sub parts If you need help with other…

Q: a +b+c+1 a + 26 + 2c + 2 Let m(a, b, c) = Set a + 26 + 3c + 4 a + 26 + 3c+d, M = {m(a, b, c) : a, b,…

A: Here we find value of d

Q: Let a, b e N. Choose all correct statements. O gcd(a, b) = gcd(-a, -b) O gcd(a, b) = gcd(a², b²) O…

A: We apply property of GCD to solve the problem

Q: Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w) and…

A: We have to check whether the statements, "If Rez&gt;Rew and Imz&gt;Imw then z&gt;w" Is true or…

Q: A CU (A - B) в) BU (C - A) с) в - (АС) BU (A - C)

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Q: A group of 90 tourists has a trip in Boracay. The island has two kinds of vehicle, the ordinary…

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Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: true. Show that (a v bc)(a Abc); but the converse is not

A: Solution:

Q: Show that ∗ : R × R → R given by           a ∗ b → a + 2b is not associative.

A: Given:Show that ∗: R × R → R given by           a ∗ b → a + 2b is not associative.