1. Consider the relation R on the set (a,b.c,d,e,f] which is defined as follows: R-[(a,a), (a,b). (a,c). (b.a). (b.c), (c.a). (c.b). (d.d), (f,f). Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Give reasons

2.Consider relation R=(A,B,C,D) with the following FDs: B → C, C > D, and D A a. List all candidate keys of R. b. Is R in 3NF? BCNF? Justify your answer

Let A = {a, b, c, d} and R = {(a, a), (b, b), (c, c), (d, d), (a, d), (d, a), (b, c), (c, b)} an equivalence relation on A. Select the following sets that are equivalence classes of R {a, b} {a} {a,b,c} O{c, b} O{a, d} {a,b,c,d} {d} {c, d}

Let R be a relation on A = {0, 1, 6, 8} and R = {(0,0), (8, 6), (6, 6), (8, 8), (1, 1), (1,0), (0, 1)}. Are the following statements true or false? 1. R is symmetric ? ? ? ? ? ? V V 2. R is transitive 3. R is reflexive 4. R is an equivalence relation 5. R is anti-symmetric 6. R is a partial order

a) Define a relation R on R (the set of all real numbers) as follows: For all x, y E R, xRy → x < y. Is R reflexive, symmetric and transitive?

Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number of tuples that the results of the following expression can have? TL(R) – S, for some list of attributes L A. n B. n-m C. max{n,m} D. n*m E. min{n,m} F. m G. n+m H. 0

Consider an equivalence relation R on X={a,b,c}. R= {(a,a), (a,c), (b,b), (c,a), (c,c) } [a]=

Hello. Please answer the attached MIPS programming question correctly by selecting the correct answer choice that translates the given C code to MIPS. You do not have to give a lengthy explanation. I just need the correct answer. *If choose the correct answer choice, I will give you a thumbs up. Thanks.

Quantifiers are called quantifiers because they express somethingabout the number of elements that satisfy a certain property. Showhow to express the following ‘quantified’ statements in predicatelogic with a unary relation symbol R. You don’t have to introduceany new quantifiers to do this, although you will need to keep inmind that the atomic formula x=yis always considered to be partof the language.(a) Exactly one x satisfies R(x).(b) At least one x satisfies R(x). (c) No more than three x satisfy R(x).(d) All but one x satisfy R(x).

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