book.rb

class Book < ApplicationRecord
  has_and_belongs_to_many :categories
  validates :categories, presence: true
end

category.rb

class Category < ApplicationRecord
  has_and_belongs_to_many :books
end

console.rb

c = Category.create title: "Some Category"
b = Book.new title: "Some Book"
unless b.valid?
  puts b.errors.inspect
end
b.categories << c
if b.valid?
  puts "book is now valid!"
end