**Title: Set Theory Exercise: Listing Elements of Sets****Instructions:** List the elements of the following sets.**a) M** - Description: The set of letters in the word "mathematics." - Note: There are not 11 elements in the set.**b) M - B** - Defined: M is as described above. - B = {a, e, i, o, u} - Operation: List elements in M that are not in B.**c) A ∪ B** - Defined: B is as above and A = {s, e, t} - Operation: Find the union of sets A and B.**d) (A - B) ⊂ C** - Description: For A and B defined above, determine if (A - B) is a subset of C. - C = The letters in the word "Sarina."**e) Aᶜ** - Description: The complement of set A when the universal set X = {a, b, c, d, ..., m}.**f) {x ∈ Reals | x² + 6x + 8 = 0}** - Description: List the real numbers x that satisfy the equation x² + 6x + 8 = 0.

Answered: M=DThe letters in the Note: There Ore…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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**Title: Set Theory Exercise: Listing Elements of Sets**

**Instructions:** List the elements of the following sets.

**a) M**
- Description: The set of letters in the word "mathematics."
- Note: There are not 11 elements in the set.

**b) M - B**
- Defined: M is as described above.
- B = {a, e, i, o, u}
- Operation: List elements in M that are not in B.

**c) A ∪ B**
- Defined: B is as above and A = {s, e, t}
- Operation: Find the union of sets A and B.

**d) (A - B) ⊂ C**
- Description: For A and B defined above, determine if (A - B) is a subset of C.
- C = The letters in the word "Sarina."

**e) Aᶜ**
- Description: The complement of set A when the universal set X = {a, b, c, d, ..., m}.

**f) {x ∈ Reals | x² + 6x + 8 = 0}**
- Description: List the real numbers x that satisfy the equation x² + 6x + 8 = 0.

Expert Solution

Step 1

As per rule we will solve only first three subparts.

$a) Given M is the set of lettes in the word' mathematics' . The word mathematics has 8 distinct letters m, a, t, h, e, i, c, s So M = {m, a, t, h, e, i, c, s}$

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