[MATH]
(e \cup f)^c = e^c \cap f^c
[/MATH]
I am struggling to prove this identity. Could someone please help me out.
Below is the kind of think i have been trying so far. But to no avail.
[MATH] e^c \cap f^c \\= e^c + f^c - e^c \cup f^c \\ = (1-e) + (1-f) - e^c \cup f^c \\ = 2-(e+f) - e^c \cup f^c \\ = (e+f)^c + 1 - e^c \cup f^c \\ \\ therefore \\ \\ e^c \cup f^c = 1 ? \\ \\ [/MATH]
pretty sure i messed up somewhere
I am struggling to prove this identity. Could someone please help me out.
Below is the kind of think i have been trying so far. But to no avail.
[MATH] e^c \cap f^c \\= e^c + f^c - e^c \cup f^c \\ = (1-e) + (1-f) - e^c \cup f^c \\ = 2-(e+f) - e^c \cup f^c \\ = (e+f)^c + 1 - e^c \cup f^c \\ \\ therefore \\ \\ e^c \cup f^c = 1 ? \\ \\ [/MATH]
pretty sure i messed up somewhere