Question

Exercise 3.3.1: Unions and intersections of sets.

Define the sets A, B, C, and D as follows:

• A = {-3, 0, 1, 4, 17}
• B = {-12, -5, 1, 4, 6}
• C = {x ∈ Z: x is odd}
• D = {x ∈ Z: x is positive}

For each of the following set expressions, if the corresponding set is finite, express the set using roster notation. Otherwise, indicate that the set is infinite.

(c)

A ∩ C

(d)

A ∪ (B ∩ C)

(e)

A ∩ B ∩ C

Answer 1

Note: there is no odd numbers in negative numbers.

The resultant sets are finite or not and it's set is mentioned

as follows,

Ans: Given: A = q -,0, 1, 4, 17 % B = { -12,-5, 1,4,67 C = { 1,3,5,7,-.- ? De 41,2,3,4,5, ---Y C. ANC = -3,0,114,17% 1 y 0861,3,5,7, -17, my Anc = { 1, 17} . Anc is finite and Anc = {1, 172 I. Au(BOC) (ene) = -12,-5,114,64 n {1,3,5,4,. --- Y AU (BAC) = 8-3,0, 1,4,174 ufig ={-3,0,1.4,17% AU (BAC) is finite and Au(BAC) = {-3,0, 1,4, 17 = A 6. Anone can be written as (ANB) n. ADB = {-3,0, 1, 4, 17 n4-12, -5, 1, 4168 (AMB)n C = $ 1,144 n { 1,3,5,7,-- - p ={ 14 (ANB) ne is finite and ADBAC =sih