MAT2611 Assignment 1 solutions 2026

MAT2611 Assignment 1 solutions 2026




Due date: Friday, 30 April 2026




ASSIGNMENT 01 – MAT2611

, Problem 1

(a)

Give an example of a set 𝐴such that there exists a set 𝐵with
𝐵 ∈ 𝐴but 𝐵 ⊈ 𝐴.

Solution:

Let

𝐴 = {{1,2},3}

Choose

𝐵 = {1,2}


• Clearly, 𝐵 ∈ 𝐴because {1, 2}is an element of 𝐴.

• To check whether 𝐵 ⊆ 𝐴:
The elements of 𝐵are 1and 2.
Neither 1nor 2is an element of 𝐴.

∴𝐵⊈𝐴


This satisfies the requirement.

(b)

Give an example of a set 𝐴such that there exists a set 𝐵with
𝐵 ⊆ 𝐴but 𝐵 ∉ 𝐴.

Solution:

Let 𝐴 = {1,2,3}

Choose

𝐵 = {1,2}


• Every element of 𝐵is contained in 𝐴, so

𝐵⊆𝐴


• However, the set {1, 2}is not an element of 𝐴.

∴𝐵∉𝐴

This satisfies the requirement.