Why can we see the Moon during the day?

We often think of the sky being dominated by two objects: the Sun during the day and the Moon at night. But we often see the moon in the sky during the day? So why do we think of the Moon and Sun being opposites and why is it that we sometimes see the Moon at night and sometimes we see it during the day?

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Farmers Almanac - http://cdn.farmersalmanac.com/wp-cont...
Sun and Moon symbol - http://multigfx.com/wp-content/upload...
Bruce Almighty Moon - http://ehads.com/wp-content/uploads/2...
The Simpsons TV show
The Spiderman cartoon
The Walking Dead