= 6. [10 points] Consider the relations R, R2, R3, R4 and properties P, P2, P3,...

 

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= 6. [10 points] Consider the relations R₁, R2, R3, R4 and properties P₁, P2, P3, P4 on N = {1,2,3,...} (i.e. all variables represent elements of IN). R1: (x, y) = R₁ R2: (x, y) = R₂ → (yx) (3z ((x|z) ^ (y|z) ^ (z < xy))) (ab (1 = ax +by)) R3: (x, y) = R3 ⇒ R4: (x, y) = R₁ ⇒ R4 (y=x²) P1: Vevyv:(((Ry) ^ (R2)) ⇒ (xR:)) P2: Vx³y³z ((xRy) ^ (xRz) ^ (y + 2)) P3: 3x (xRx) P4: Vay ((x Ry) ^ (x + y)) Determine whether or not each relation satisfies each property, giving your answers as 'Yes' or 'No' in the table below (you can copy the table by hand onto your paper, please keep the same order for the rows and columns!). You do not need to provide any reasoning for your answers. = 6. [10 points] Consider the relations R₁, R2, R3, R4 and properties P₁, P2, P3, P4 on N = {1,2,3,...} (i.e. all variables represent elements of IN). R1: (x, y) = R₁ R2: (x, y) = R₂ → (yx) (3z ((x|z) ^ (y|z) ^ (z < xy))) (ab (1 = ax +by)) R3: (x, y) = R3 ⇒ R4: (x, y) = R₁ ⇒ R4 (y=x²) P1: Vevyv:(((Ry) ^ (R2)) ⇒ (xR:)) P2: Vx³y³z ((xRy) ^ (xRz) ^ (y + 2)) P3: 3x (xRx) P4: Vay ((x Ry) ^ (x + y)) Determine whether or not each relation satisfies each property, giving your answers as 'Yes' or 'No' in the table below (you can copy the table by hand onto your paper, please keep the same order for the rows and columns!). You do not need to provide any reasoning for your answers.

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Here R2R say Relation is Rxy lcmxy That is lcm of two netural number is strictly less than t... View the full answer