Prove or disprove the following equivalence claim.
(r ∧ s ∨ ¬t) ⇒ q ≡ ( ¬r ∧ t) ∨ (¬s ∧ t) ∨ q
Prove or disprove the following equivalence claim. (r ∧ s ∨ ¬t) ⇒ q ≡ ( ¬r...
9. Let R an equivalence relation. Prove or disprove that R:R is an equivalence relation
(1) Suppose R and S are reflexive relations on a set A. Prove or disprove each of these statements. (a) RUS is reflexive. (b) Rn S is reflexive. (c) R\S is reflexive. (2) Define the equivalence relation on the set Z where a ~b if and only if a? = 62. (a) List the element(s) of 7. (b) List the element(s) of -1. (c) Describe the set of all equivalence classes.
z 또 Q then re Q Exercise 10. Prove or disprove: If z 또 Q then re Q Exercise 10. Prove or disprove: If
a) Prove or disprove: if S,TELluv) then trace ('st) = trove's) tracel T) b) Prove or disprove, if S.TELIVE) then det (5+ 7) = det (5) + det (7)
Prove or disprove the following. (a) R is a field. (b) There is an additive identity for vectors in R^n. (If true, what is it?)........ 1. Prove or disprove the following. (a) R is a field (b) There is an it?) additive identity for vectors in R". (If true, what is (c) There is a is it? multiplicative identity for vectors in R". (If true, what (d) For , , (e) For a, bE R and E R", a(b) =...
Prove/disprove for any regular expressions R and S: (a) (R + S)∗S = (R∗S)∗ (b) (R + S)∗ = (R∗S)∗ Note: when disproving a statement, you must give a concrete example of R and S, meaning a definition of R and S over some chosen alphabet.
prove the equivalence without using truth tables P → (Q → S) ≡ (P ∧ Q) → S.
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
Consider the empty set as a relation, R, on any non-empty set S. Prove or disprove: R is transitive.
Prove or Disprove #3 (d) For each of the following, prove or disprove: iii) There is an element of X × Y with the form (a, 3a) (d) For each of the following, prove or disprove: iii) There is an element of X × Y with the form (a, 3a)