Question

Find a counterexample to show that we don't always have equality.

Answer 1

Hello your question is incomplete below is the complete question

Let R be a relation from A to B and S a relation from B to C.

(a) Prove that .
`Dom(S \circ R) \subseteq Dom(R)`

(b) Find a counterexample to show that we don’t always have equality.

answer : (b) Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]

hence: Dom ( S o R ) ≠ Dom ( R )

Explanation:

Note : R ⊆ A * B and S ⊆ B * C

A) To prove that
`Dom(S \circ R) \subseteq Dom(R)`

we take note that : S o R ⊆ A x C

ATTACHED BELOW IS THE REMAINING PART OF THE SOLUTION

B) A counterexample to show that we don't always have equality

attached below is a assumptions and solution on how we arrived at the value below

Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]

hence: Dom ( S o R ) ≠ Dom ( R )