Have to prove this... :/

R ° (S ∩ T) ⊆ (R ° S) ∩ (R ° T)

Anyone here who could help?

What does ° stand for ?
Union ? Symmetric difference ? ...
Be more precise when using non-normalized notation.

Isnt it standard notation for composed?

Maybe thats better:

R ∘ (S ∩ T) ⊆ (R ∘ S) ∩ (R ∘ T)

and ∘ stands for composition.

Applications / functions can be eventually composed. Not sets...

Does this help

Maybe this ?

R ⊆ X x Y
S ⊆ Y x Z
T ⊆ Y x Z

Let (x,z) in R ∘ (S ∩ T).

There exists y in Y such that :
(x,y) lies in R
(y,z) lies in (S ∩ T), which means that it lies in S and also in T.

Since (x,y) lies in R and (y,z) lies in S, we can say that (x,z) lies in R ∘ S.
Since (x,y) lies in R and (y,z) lies in T, we can say that (x,z) lies in R ∘ T.
Hence, (x,z) lies in (R ∘ S) ∩ (R ∘ T).

Conclusion : R ∘ (S ∩ T) ⊆ (R ∘ S) ∩ (R ∘ T).

And you can't replace ⊆ with = , since having (x,z) in (R ∘ S) ∩ (R ∘ T) means :
- there exists y₁ such that (x,y₁) ∈ R and (y₁,z) ∈ S
- there exists y₂ such that (x,y₂) ∈ R and (y₂,z) ∈ T
but there is no reason why y₁ should equal y₂, so no reason why there should exist y such that (x,y) ∈ R and (y,z) ∈ S and (y,z) ∈ T.