C, b,$2,1, 2, 3, 7,0) and let R he an eeivolence relatin by Let an eqivalence relation by all Find A/ C, b,$2,1, 2, 3, 7,0) and let R he an eeivolence relatin by Let an eqivalence relation b...
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R 3 c) R 4 d) R 5 Consider the same relation R as above. List all walks in R staring from node 3 that correspond to the edges in a) R 2 b) R 3
4. [3 marks] Let R be a relation on a set A. Let A {1,2, 3, X, Y} and R = {(1, 1), (1,3), (2,1), (3, 1), (1, X), (X, Y)} (a) What is the reflexive closure of R? (b) What is the symmetric closure of R? (c) What is the transitive closure of R?
16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b) R(c, d) if and only if a c and b 3 d for all (a, b), (c, d)E A. Prove that R is a partial ordering on A that is not a total ordering. 16. (8 points) Let Z be the integers and let A - Zx Z. Define the relation R on A by (a, b)...
8) Let R be a relation on the set A = {a, b, c} defined by R= {(a, a),(a, b), (a, c), (b, a), (b, b)}. (3 points)_a) Find Mr, the zero-one matrix representing R (with the elements of the set listed in alphabetical order). (2 points)_b) Is R reflexive? If not, give a counterexample. (2 points)_c) Find the symmetric closure of R. (3 points)_d) Find MR O MR.
Please answer all!! 17. (a) Let R be the relation on Z be defined by a R b if a² + 1 = 62 + 1 for a, b e Z. Show that R is an equivalence relation. (b) Find these equivalence classes: [0], [2], and [7]. 8. Let A, B, C and D be sets. Prove that (A x B) U (C x D) C (AUC) Ⓡ (BUD).
Let a. Find at (2,1) b. Find the directional derivative of f at (2,1) in the direction of -i+3j f(:,y) = xy - 1 We were unable to transcribe this image
Let A = ( a, b, c, d ) and let ( A, R ) be a posset where R is a Relation on A defined by: R is reflexive c ≤ d a ≤ c a ≤ b a ≤ d b ≤ d Find H(A) Is (A, R) a lattice? If you answer no, give a counterexample. If you answer yes, give a brief justification as to why (no formal proof needed). Is (A,R) a Boolean algebra? Give...
1) Consider a relation R(A,B) with r tuples, all unique within R, and a relation S(B,C) with s tuples, all unique within S. Let t represent the number of tuples in R natural-join S. What is the value range of t? What is the value of t for R natural-join R (assuming no null values in R)? Explain your answer.
Let R ⊆ {1, 2, 3, 4} × {1, 2, 3, 4} be the relation R = {(1, 3),(1, 4),(2, 2),(2, 4),(3, 1),(3, 2),(4, 4)}. (a) Compute R −1 . (b) Compute the relations R ∪ R −1 and R ∩ R −1 , and check that they are symmetric. 7.1.3 Let RC 1,2,3,4) x 1,2,3,4) be the relation (a) Compute R-1 (b) Compute the relations RUR-1 and RnR-1, and check that they are symmetric.
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.