1. Find A × B if
(a) A = {1, 2} and B = {5, 6}
(b) A = {2, 5} and B = {4, 6}
(c) A = {3, 4} and B = {a, b}
(d) A = {5, 7} and B = {c, d}

2. If A = {2, 4}, B = {3, 2} and C = {1, 5}, find the following
(a) A × A
(b) B × B
(c) C × C
(d) A × B
(e) B × C
(f) A × C
(g) C × B
(h) C × A

In this question, we are asked to find the Cartesian product of sets, which is a fundamental concept in set theory. The Cartesian product of two sets A and B, denoted as A × B , is the set of all ordered pairs ( a , b ) where a is an element of A and b is an element of B.

Finding A × B:
(a) A = {1, 2} and B = {5, 6}
To find A × B , we list all possible ordered pairs:


A × B = {( 1 , 5 ) , ( 1 , 6 ) , ( 2 , 5 ) , ( 2 , 6 )}
(b) A = {2, 5} and B = {4, 6}

[tex]A \times B[/tex] is:

A × B = {( 2 , 4 ) , ( 2 , 6 ) , ( 5 , 4 ) , ( 5 , 6 )}
(c) A = {3, 4} and B = {a, b}

[tex]A \times B[/tex] is:

A × B = {( 3 , a ) , ( 3 , b ) , ( 4 , a ) , ( 4 , b )}
(d) A = {5, 7} and B = {c, d}

[tex]A \times B[/tex] is:

A × B = {( 5 , c ) , ( 5 , d ) , ( 7 , c ) , ( 7 , d )}

Finding Cartesian Products of Specific Combinations:
(a) A = { 2 , 4 } , A × A :


A × A = {( 2 , 2 ) , ( 2 , 4 ) , ( 4 , 2 ) , ( 4 , 4 )}
(b) [tex]B = \{3, 2\}, B \times B[/tex]:

B × B = {( 3 , 3 ) , ( 3 , 2 ) , ( 2 , 3 ) , ( 2 , 2 )}
(c) [tex]C = \{1, 5\}, C \times C[/tex]:

C × C = {( 1 , 1 ) , ( 1 , 5 ) , ( 5 , 1 ) , ( 5 , 5 )}
(d) [tex]A \times B[/tex]:

A × B = {( 2 , 3 ) , ( 2 , 2 ) , ( 4 , 3 ) , ( 4 , 2 )}
(e) [tex]B \times C[/tex]:

B × C = {( 3 , 1 ) , ( 3 , 5 ) , ( 2 , 1 ) , ( 2 , 5 )}
(f) [tex]A \times C[/tex]:

A × C = {( 2 , 1 ) , ( 2 , 5 ) , ( 4 , 1 ) , ( 4 , 5 )}
(g) [tex]C \times B[/tex]:

C × B = {( 1 , 3 ) , ( 1 , 2 ) , ( 5 , 3 ) , ( 5 , 2 )}
(h) [tex]C \times A[/tex]:

C × A = {( 1 , 2 ) , ( 1 , 4 ) , ( 5 , 2 ) , ( 5 , 4 )}
By understanding how to form these products, you'll be able to handle more complex problems involving Cartesian products and relations.

Answered by OliviaMariThompson | 2025-07-07