MAT2611
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
a).
Given ∶ A = {a, b, c} and B = {1, 2}
i).
A × B = {(x, y) ∶ x ∈ A and y ∈ B }
A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}
ii).
B × A = {(y, x) ∶ x ∈ A and y ∈ B }
B × A = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}
We can see that A × B is not equal to B × A
b).
Given: |A| = n and |B| = m then
|A × B| = |A| × |B|
=n×m
= nm
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
a).
Given ∶ A = {a, b, c} and B = {1, 2}
i).
A × B = {(x, y) ∶ x ∈ A and y ∈ B }
A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}
ii).
B × A = {(y, x) ∶ x ∈ A and y ∈ B }
B × A = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}
We can see that A × B is not equal to B × A
b).
Given: |A| = n and |B| = m then
|A × B| = |A| × |B|
=n×m
= nm
