Question

find A×B,A×A and B×A A=B={p,q}

Answer 1

concept : for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

product can be written in set builder notation as $\bf{A\times B}=\{(a,b)|a\in A\:\:\textbf{and}\:\:b\in B\}$

given, A = B = {p, q}

A × B = {p , q} × {p, q}

= {(p, p), (p, q), (q, p), (q, q)}

A × A = {p, q} × {p, q}

= {(p, p), (p, q), (q, p), (q, q)}

here it is clear that A × B = A × A = {(p, p), (p, q), (q, p), (q, q)}

Answer 2

Step-by-step explanation:

A------------P----------Q-----------B