MAT3707 Assignment 2 (710554 ) Due 18 July 2025

MAT3707
Assignment 2
Unique No: 710554
Due 18 July 2025

, MAT3707

Assignment 2

Unique No: 710554

Due July 18, 2025



Question 1

Let Abe a set with melements and Ba set with nelements.

Part (i): Number of Elements in ( A×{ A})∪( B×{ B}) and Comparison with A∪ B

• Problem Statement: Find the number of elements in the set ( A×{ A})∪ ( B× { B}).
Explain how it differs from A∪ B, with examples.

• Step 1: Understand the Sets

– Let A= { a1 ,a2 ,...,am}, so | A| = m, and B= { b1 ,b2 ,...,bn}, so | B| = n.

– A× { A} = {( ai ,A) : ai∈ A}, where { A} is a singleton containing the set A.

– B× { B} = {( bj ,B) : bj∈ B}.

– We need to compute |( A× { A}) ∪ ( B× { B})| and compare with | A∪ B|.

• Step 2: Compute | A× { A}|

– The Cartesian product A× { A} has pairs ( ai ,A).

– Since | A| = mand |{ A}| = 1, the number of elements is:

| A× { A}| = | A| · |{ A}| = m· 1 = m

• Step 3: Compute | B× { B}|

– Similarly, B× { B} has pairs ( bj ,B).

– Since | B| = nand |{ B}| = 1, the number of elements is:

| B× { B}| = | B| · |{ B}| = n· 1 = n