Draw Lattice Diagram for K: Solving Algebra I Mapping Homework

[rbzima]

Homework Statement

K = {x C S7 | 2x=2, {1,4}x={1,4}, {1,5,7}x={1,5,7}}.
Draw Lattice Diagram for K.2. The attempt at a solution

I've looked at this for about 30 minutes and came to the conclusion that there are 140 unique solutions to this mapping, and I know for a fact that the professor does not want us to draw all 140 of these. Essentially, I found that 3!3!2!2! - 4 = 140. At this point I have no idea how to express this in a far easier form then what is given and I'm not sure where to go with the Lattice Diagram. Help would def be appreciated.

 

[rbzima]

Never mind. Mods can delete this thread because I've figured it out. The statement above states that {1,4}x = {1,4}, but similarly {1,5,7}x = {1,5,7}, which implies that for this statement to be true, 1 maps to 1, and 4 maps to 4, therefore all we are left with is combinations of {5,7} and {3,6}, which are simply (57)(36), I(36), (57)I, and I sub 7.