one\'s enemy is one\'s friend\" mean about the relations E and F? Suppose R is a

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one's enemy is one's friend" mean about the relations E and F? Suppose R is a relation from A to B and 5 is a relation from B to C Prove that Dom(S o R) Dom(R). Prove that if Ran(R) Dom(S) then Dom(S o R) = Dom(R). Formulate and prove similar theorems about Ran(S o R). Suppose R and S are relations from A to B. Must the following statements be true? Justify your answers with proofs or counterexamples. R Dom(R) x Ran(R). If R S then R-l S-1. (R U S)-1 = R-1 US-1. Suppose R is a relation from A to B and S is a relation from B to C. Prove that iff Ran (R) and Dom (S) are disjoint.

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