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Let A = {1, 2, 3, 4, 5} then define a relation R on A as (a.b)∈R iff a≤b and Relation Ton A as (a,b)∈T iff a/b. Represent R by an matrix. Is R Reflexive? Transitive? Give a valid reason for your answer. Is T Antisymmetric? Give a val…
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For each of the following sets, determine whether 2 is an element of that set. (a){x∈R|x is an integer greater than 1} (b){x∈R|x is the square of an integer} (c){2 ,{2}} (d){{2},{{2}}} (e){{2},{2 ,{2}}} (f){{{2}}}
(i) Determine whether each of these statements is true or false. (a) 0∈∅ (b)∅∈{0} (c){0}⊂∅ (d)∅⊂{0} (e){0}∈{0} (f){0}⊂{0} (g){∅}⊆{∅} (ii) Determine whether these statements are true or false. (a)∅∈{∅} (b)∅∈{∅,{∅}} (c){∅}∈{∅} (d){∅}∈{{…
(a) Use a Venn diagram to illustrate the relationships A ⊆ B and B ⊆ C. (b) Use a Venn diagram to illustrate the relationships A ⊂ B and B ⊂ C. (c) Use a Venn diagram to illustrate the relationships A ⊂ B and A ⊂ C. (d) Suppose that A…
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(i) Show that if A ⊆ C and B ⊆ D, then A×B ⊆ C ×D (ii) Let A ={a , b , c ,d}and B ={y , z}. Find (a) A×B (b) B×A
(i) Let A ={a , b , c}, B ={x , y}, and C ={0 , 1}. Find (a) A×B×C (b) C ×B×A (c) C ×A×B (d) B×B×B (ii) Let A ={1 , 2 , 3 , 4 , 5}and B ={0 , 3 , 6}. Find (a) A∪B (b) A∩B (c) A−B (d) B−A (iii) Let A ={a , b , c , d ,e}and B ={a , b …
Determine whether the following preposition is tautology, contradiction or contingency and explain the answer by your own words. (p↔q ) ⊕ ¬(q→p)
A set S is cardinally majorizable by a set T iff there exists a(n) ______________ from T to S.
Which of the following sets have the same cardinality? Select all that apply. LaTeX: \mathbb{N} N [0,1] LaTeX: \mathbb{R} R (0,1)
1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and are respectively 72, 28 and 13, then find the cardinality of the set .
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9. (i) Prove the identity laws in Table 1 by showing that (a) A ∪ ∅ = A (b) A ∩ U = A (ii) Prove the domination laws in Table 1 by showing that (a) A ∪ U = U (b) A ∩ ∅ = ∅ (iii) Prove the idempotant laws in Table 1 by showing that (a)…
10. Let A , B, and C be sets. Show that(a) (A ∪ B) ⊆ (A ∪ B ∪ C) (b) (A ∩ B ∩ C) ⊆ (A ∩ B) (c) (A − B) − C ⊆ (A − C) (d) (A − C) ∩ (C − B) = ∅ (e) (B − A) ∪ (C − B) = ∅
11. Show that if A and B are sets, then (a) A − B = A ∩ B (b) (A ∩ B) ∪ (A ∩ B) = A
12. Draw the Venn diagrams for each of these combinations of the sets A , B , and C. (a) A ∩ (B ∪ C) (b) A ∩ B ∩ C (c) (A − B) ∪ (A − C) ∪ (B − C)
b) In a large city, 8% of the inhabitants have contracted a particular disease. A test for this disease is positive in 80% of people who have the disease and is negative in 80% of people who do not have the disease. What is the probab…
Robyn decides to organize a hiking trip and invites her friends - Dylan, Linda and Dominic to join her. On the days leading to the hike, her three friends say the following:Two Days Before the hike:Dylan: Dominic is going to the hike.…

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Question ID: mtid-5-stid-8-sqid-384-qpid-271