Definition: The Cartesian Product of two sets A and B, denoted by. A x B is the set of ordered pairs (a,b) where a EA andbE B Ax B = {(a, b) |a € A1b € B}
Example:
A = {a,b] B = {1,2,3}
A x B = {(a,1), (a,2), (a,3), (b, 1), (b, 2), (b,3)
]Q1. Is it possible that: (A c B)л (B c 4) =› (| 4|=| B |= 0) ? Algebraically prove your
answer.
Q2. Algebraically prove that: ((4 = {0}) ^ (B = 0)) = ((| A > BI) V (A + B)).
Q3. Algebraically prove that: if 3{(a,b), (b, a)} c Ax B such that (a, b) = (b, a) then
3C c A where Cc B.