Create a new document. Use the elliptical marquee tool to create a blue circle.
Load the selection of the layer and move it over until it looks like that below.
After you delete this selection, it will look like this below.
Use the elliptical marquee tool to create a green oval.
Move this selection up a bit
Delete the selection, and rotate the layer a little through the use of the transform tool.
Load the selection of the green layer. Then go to Layer > Modify > Expand. Expand by 5 pixels. Then select the original blue layer, and delete the selection.
Use the elliptical marquee tool to create a magent oval approximately the same width as the green one.
Using the same method in the last two steps, you will get the resultant graphic below.
Once again, select the elliptical marquee tool and fill an oval selection with orange.
Transform the selection a little bit and move it over. Delete that portion of the layer.
And the result is below.
Move and rotate (Ctrl + T) the layers a little bit to straighten everything out.
Complete step #7 except this time, use the orange layer first, and then delete from the blue layer.
To finalize your logo, add your company text below with any other symbols you wish. The final product is below.
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