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    I have no ideas. This is the last question in the Maths homework I have today. The other problems related to groups and sets are all solved, save this difficult one...Again, I have no ideas... :confused:

    Consider two sets S and T with a mapping a: S --> T. If A and B are subsets of S, show that a (A U B) = a (A ) U a (B )

    PS: Don't laugh at me; I'm just 15 and I'm the youngest student in my maths class. One more time, I have absolutely NO ideas on how to solve this problem. :embarasse
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    Suppose that y is a(A u B). Then there is an x in A u B such that a(x) = y. We know that (i) x is in A, or (ii) x is in B.
    • If (i) is true then y is in a(A). So y is in a(A) u a(B).
    • If (ii) is true then y is in a(B). So y is in a(A) u a(B).

    We have proved that y is in a(A) u a(B).

    --

    Suppose that y is in a(A) u a(B). Then (i) y is in a(A), or (ii) y is in a(B).
    • If (i) is true then there is an x in A such that a(x) = y. Since x is in A u B, y is in a(A u B).
    • If (ii) is true then there is an x in B such that a(x) = y. Since x is in A u B, y is in a(A u B).

    We have proved that y is in a(A u B).

    --

    We have proved that if y is in a(A u B) then y is in a(A) u a(B), and vice versa. So a(A u B) = a(A) u a(B)
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    (Original post by Jonny W)
    Suppose that y is a(A u B). Then there is an x in A u B such that a(x) = y. We know that (i) x is in A, or (ii) x is in B.

    * If (i) is true then y is in a(A). So y is in a(A) u a(B).
    * If (ii) is true then y is in a(B). So y is in a(A) u a(B).

    We have proved that y is in a(A) u a(B).

    --

    Suppose that y is in a(A) u a(B). Then (i) y is in a(A), or (ii) y is in a(B).

    * If (i) is true then there is an x in A such that a(x) = y. Since x is in A u B, y is in a(A u B).
    * If (ii) is true then there is an x in B such that a(x) = y. Since x is in A u B, y is in a(A u B).

    We have proved that y is in a(A u B).

    --

    We have proved that if y is in a(A u B) then y is in a(A) u a(B), and vice versa. So a(A u B) = a(A) u a(B)
    This makes some sense. Thanks a lot.
 
 
 
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