(a,b,c), (d, e, f) = AX AX A, (a,b,c) (d,e,f) a ≤d, b ≤e, and c
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- Let A {0,1,2} and the partial order relation R be defined on the set of A x A as follows: For V(a,b), (c,d) e A × A, (a,b)R(c,d) → aLet A = {0,1,2,3} and R a relation over A: R = {(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.If R and S are partial orders, then must ROS be a partial order? If not, explain why. Where is the exclusive or (XOR) operator.Let A = {0,1,2} and the partial order relation R be defined on the set of A × A as follows: For V(a, b), (c, d) E A × A, (a,b)R(c,d) → a < c and b < d |(a) Draw the Hasse diagram for R. (b) Write the minimal, maximal, least and greatest elements of R.Let A = {0, 1, 2} and the partial order relation R be defined on the set of A × A as follows:For ∀(a, b),(c, d) ∈ A × A, (a, b)R(c, d) ⇐⇒ a ≤ c and b ≤ d(a) Draw the Hasse diagram for R.(b) Write the minimal, maximal, least and greatest elements of R.A relation R on a set S is called a partial order if it satisfies three properties (one of which is new to us): I R is reflexive. II R is anti-symmetric: Vr, y E S, (xRy A yRx) = x = y. III R is transitive. Which of the following relations is a partial order on the set S = N? Select only one answer. (a) xRy = a² = y? (b) xRy + x|y (c) rRy + xy is even (d) xRy x + y is a prime number (e) xRy + xy > 3Atleast do 4 subpart Let R be the partial order relation defined onLet A = {0, 1, 2} and the partial order relation R be defined on the set of A × A asfollows:For ∀(a, b),(c, d) ∈ A × A, (a, b)R(c, d) ⇐⇒ a ≤ c and b ≤ d(a) Draw the Hasse diagram for R.(b) Write the minimal, maximal, least and greatest elements of R.Let A Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (z, w) in A, (z, y)R(z, w) I+w = z+y. %3D List five elements in [(1,1)]. List five elements in [(1, 2).SEE MORE QUESTIONS