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    Let A ={1,2}, B={1,2,3}

    Describe explicitly

    i) all mappings g:A->B
    ii) all mappings g:B->A
    iii) all mappings g:B->B

    Moreover, in each case say which mappings are
    a) injective
    b) surjective
    c) bijective

    Let m, n be fixed positive integers. How many mappings are there of the form

    g:{1,.....,m}->{1,.....,n}?

    Thanks!
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    just draw all possible ways of mapping
    with g : {1, ..., m} -> {1,..., n} there are nm mappings
    I think
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    (Original post by BCHL85)
    just draw all possible ways of mapping
    with g : {1, ..., m} -> {1,..., n} there are nm mappings
    I think
    wicked thanks.

    without the use of truth tables, can you prove in detail the following identities between sets A,B,C,D:

    i) A u (BnC)=(AuB) n (AuC)
    ii) A-(BnC)=(A-B) u (A-C)
    iii) (AxB)-(CxD)=(A-C)xB u Ax(B-D)

    Is it true in general that:
    (AuB)x(CuD)=(AxC)u(BxD)?

    If so, prove. If not, give a counterexample.
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    (Original post by CharlyH)
    wicked thanks.

    without the use of truth tables, can you prove in detail the following identities between sets A,B,C,D:

    i) A u (BnC)=(AuB) n (AuC)
    ii) A-(BnC)=(A-B) u (A-C)
    iii) (AxB)-(CxD)=(A-C)xB u Ax(B-D)

    Is it true in general that:
    (AuB)x(CuD)=(AxC)u(BxD)?

    If so, prove. If not, give a counterexample.
    To prove identities between sets, just use an 'argument' that proves each is a subset of other.
    For example, the first part of (i) is:
    Suppose x \in A U (B n C). Then x \in A or x \in B n C. That is, x \in A or x \in B and x \in C. Hence x \in A or x \in B and x \in A or x \in C. Hence x \in AuB and x \in AuC. Thus x \in (AuB)n(AuC)
 
 
 
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