A∨B∧C ⇔ (A or B) and (A or C)
Proof the first direction
If A or B and C:
If A:
A
A or B
A or C
(A or B) and (A or C)
A implies (A or B) and (A or C)
If B and C:
B and C
B
C
A or C
B
A or B
A or C
(A or B ) and (A or C)
B and C implies (A or B ) and (A or C)
A or B and C
A implies (A or B) and (A or C)
B and C implies (A or B ) and (A or C)
A∨B∧C implies (A or B) and (A or C)