Suppose that A, B, C and D are sets, R is a relation between A and B

(i.e., R ⊆ A x B), S is a relation between B and C and T is a relation

between C and D. Show the following:

(a) R ¤ (S ¤ T) = (R ¤ S) ¤ T.

(b) (R ¤ S)⁻¹ = S⁻¹ ¤ R⁻¹ .

Please help

Printable View

- September 19th 2011, 01:09 PMhabsfan31Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show that
Suppose that A, B, C and D are sets, R is a relation between A and B

(i.e., R ⊆ A x B), S is a relation between B and C and T is a relation

between C and D. Show the following:

(a) R ¤ (S ¤ T) = (R ¤ S) ¤ T.

(b) (R ¤ S)⁻¹ = S⁻¹ ¤ R⁻¹ .

Please help - September 19th 2011, 01:27 PMPlatoRe: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show
- September 19th 2011, 01:33 PMhabsfan31Re: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show
Yup, sorry bout that

- September 19th 2011, 01:42 PMPlatoRe: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show
If think then you have it backwards.

exists but does not.

Because relates and relates .

So it must be .

Unless your text material is completely non-standard.

It is usual for compositions to read right to left.

Post Script

Do you understand what I have posted?

If then if then

exists BUT may not.

By definition .

That means that