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# Mappings again! watch

1. 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!
2. just draw all possible ways of mapping
with g : {1, ..., m} -> {1,..., n} there are nm mappings
I think
3. (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.
4. (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 . Then or . That is, or and . Hence or and or . Hence and . Thus

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Updated: November 13, 2005
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