Answer to Question #306673 in Discrete Mathematics for ibrahim

Question

If R⊆S, then T∘R ⊆ T∘S and R∘T ⊆ S∘T

Answer 1

Solution

Suppose, $(a, b) ∈ T ο R$

Then there is an element $c ∈ A$ , such that $(a, c) ∈ R$ and $(c, b) ∈ T$

Now since, $R ⊆ S$ , $(a, c) ∈ S$ and thus $(a, b) ∈ T ο S$

Hence, we can write,

$T ο R ⊆ T ο S$