Discrete Mathematics Answers

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) = ∅

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) A ∪ A = A (b) A ∩ A = A
(iv) Prove the complement laws in Table 1 by showing that

(a) A ∪ A = U (b) A ∩ A = ∅

need help with solving assignment

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.

(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 , c , d , e , f , g , h}. Find
(a) A∪B
(b) A∩B
(c) A−B
(d) B−A