Question

assume \(S=\{x,y,z\}\) and \(T=\{1,2,3\}\).

how many mappings are there from \(S\) onto \(T\)?
i think \(3!=6\)

how many one-to-one mappings are there from \(S\) to \(T\)?
i think \(3!=6\) again

how many mappings are there from \(S\) to \(\{1,2\}\)?
i think \(2^3=8\)

how many mappings are there from \(S\) onto \((1,2)\)?
i think that there are none\[\]am i right?

Answer 1

how many mappings are there from S onto T? For every member of S, there are 3 choices. As S has three members, that means there are 3^3 = 27 possible functions.

Answer 2

thats what i thot at first but thenwouldnt be onto :(

Answer 3

Sorry, yes. Onto. I was thinking of it ... never mind. Yes. 3!

how many one-to-one mappings are there from S to T?
i think 3!=6.

yes, because you constrained on what you can choose.

Answer 4

how many mappings are there from S to {1,2}?
i think 2^3=8

Yes

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how many mappings are there from S onto (1,2)?
i think that there are none

(1,2) is the open interval? Then surely there are infinitely many.

Answer 5

yes is interval of real number but is also onto so i cant use all members of the codomain :(

Answer 6

or can i? if it was not onto thn itd be infinite?

Answer 7

I made the same mistake again. Onto, not to.

You are right.

Answer 8

thank u very much mr james i confirm now )))))