{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# h6 - ∼ is an equivalence relation Question 4 Let R be the...

This preview shows page 1. Sign up to view the full content.

HOMEWORK 6 Question 1. Prove that if A , B and C are any sets, then A × ( B C ) = ( A × B ) ( A × C ) . Question 2. (a) Prove that if A , B , C and D are any sets, then ( A × B ) ( C × D ) ( A C ) × ( B D ) . (b) Give an example of sets A , B , C and D such that ( A × B ) ( C × D ) = ( A C ) × ( B D ) . Question 3. Let S = { ( a, b ) | a, b Z , b = 0 } and let be the relation defined on S by ( a, b ) ( c, d ) iff ad = bc. Prove that
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∼ is an equivalence relation. Question 4. Let R be the relation on R r { } deﬁned by a R b iff a b ∈ Q or a-b ∈ Q . Determine whether R is an equivalence relation. ( Hint: You may make use of the fact that √ 2 / ∈ Q .) 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online