I would define design as a way in which people provide visual representations and solutions to problems. The word design can be used to describe many things such as print, movies, clothes and architecture.
I define culture as the views and values someone may have based on their surroundings and the way in which they were brought up. Culture can be influenced by many things such as family and society. Culture can refer to a personal view or a public one. People grow up in a certain family culture that influences who they are. At the same time, whole countries have cultures that also influence people.
I define language as the way in which people communicate with other people. Some times, people use the same language to communicate and therefore can understand each other. Other times, two people's language can be quite different and therefore communication is not successful or is very hard.
In many instances, design, culture and language intersect with each other. One someone designs something, their culture and language affect how they design it. For example, if I were to create a poster to promote a concert, my design solution may be quite different from someone who designed a poster for the same concert in Paris. The differences in our culture and language would lead the poster to be different.