Youth A, B, C, D and E from a village applied for employment in a housing maintenance company. According to their respective expertise, five of them were employed as welders, bricklayers, electricians, carpenters and plumbers. It is known that each of them does only one type of work, and one of their five people does each type of work, and it is also known that: (1) if A works as a welder, C works as a carpenter; (2) if one of B and D works as a plumber, then A works as a welder; (3) C or works as a bricklayer, or an electrician.
If E works as a bricklayer, it can be inferred that A works as a plumber.