Discrete Mathematics Answers

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. Dominic: Linda is not going to the hike.Linda: Dylan will go to the hike if, and only if, I do.The Day Before the hike:Dylan: Linda will go to the hike if, and only if, I don't go. Dominic: An even number out of the three of us are going to the hike.Linda: Dylan is going to the hike.The Day of the hike:Dylan: It is not yet 2020. Dominic: Dylan will go to the hike if, and only if, I do.Linda: At least one of the three of us is not going to the hike. Robyn also knows that out of Dylan, Dominic, and Linda:One of them never lies.One lies on days of the month that are divisible by 2, but is otherwise truthful.The remaining one lies on days of the month that are divisible by 3, but is otherwise truthful.Can you figure out who is going to attend?

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. Dominic: Linda is not going to the hike.Linda: Dylan will go to the hike if, and only if, I do.The Day Before the hike:Dylan: Linda will go to the hike if, and only if, I don't go. Dominic: An even number out of the three of us are going to the hike.Linda: Dylan is going to the hike.The Day of the hike:Dylan: It is not yet 2020. Dominic: Dylan will go to the hike if, and only if, I do.Linda: At least one of the three of us is not going to the hike. Robyn also knows that out of Dylan, Dominic, and Linda:One of them never lies.One lies on days of the month that are divisible by 2, but is otherwise truthful.The remaining one lies on days of the month that are divisible by 3, but is otherwise truthful.Can you figure out who is going to attend?

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 probability that a person for whom the test result
is positive has the disease?

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)

11. Show that if A and B are sets, then
(a) A − B = A ∩ B
(b) (A ∩ B) ∪ (A ∩ B) = 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) = ∅

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 .

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)

A set S is cardinally majorizable by a set T iff there exists a(n) ______________ from T to S.