Option Strict On

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Imports System

Imports System.Linq

Public Module Module1

    Public Sub Main()

        Dim policies() As Policy = {

            New Policy() With {.ID = 1, .HouseholdId = 1, .PolicyType = "Auto"},

            New Policy() With {.ID = 2, .HouseholdId = 1, .PolicyType = "Home"},

            New Policy() With {.ID = 3, .HouseholdId = 2, .PolicyType = "Auto"}

            }

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        'Return those with auto but not home

        Dim audit() As Integer = (From p As Policy In policies

            Group By HouseholdId = p.HouseholdId Into g = Group

            Where g.Any(Function(grouped) grouped.PolicyType = "Auto") Andalso Not g.Any(Function(grouped) grouped.PolicyType = "Home")

            Select g.FirstOrDefault().HouseholdId).ToArray()

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        Console.WriteLine("HouseholdId's: " & String.Join(", ", audit))

    End Sub

End Module

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Public Class Policy

    Public Property ID As Integer

    Public Property HouseholdId As Integer

    Public Property PolicyType As String

End Class