I need help with part (f). I know the answer is "P is a partition of A", I'm just unsure of how to formally prove this. For the given set A, determine whether P is a partition of A.(a) A = {1, 2, 3, 4}, P = {{1, 2}, {2, 3}, {3, 4}}(b) A = {1, 2, 3, 4, 5, 6, 7}, P = {{1, 2}, {3}, (4, 5}}(c) A = {1, 2, 3, 4, 5, 6, 7}, P = {{1, 3}, {5, 6}, {2, 4}, {7}}(d) A = N, P = {1, 2, 3, 4, 5} U {n € N: n > 5}(e) A= R, P = (-0, –1) U[-1, 1] U (1, )(f) A = R, P = {S,: y e R and y > 0}, where S, = {xe R: x < y}%3D%3D%3D%3D

Name: I need help with part (f). I know the answer is "P is a partition of A
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: I need help with part (f). I know the answer is "P is a partition of A", I'm just unsure of how to formally prove this. For the given set A, determine whether P is a partition of A.(a) A = {1, 2, 3, 4}, P = {{1, 2}, {2, 3}, {3, 4}}(b) A = {1, 2, 3, 4

Given: A=ℝ, P=Sy:y∈ℝ and y>0, where Sy=x∈ℝ: x<y. Observe the partition P=Sy:y∈ℝ and y>0: For y=0.1, P1=S0.1=x∈ℝ: x<0.1. That is, this set consists of all elements of ℝ below 0.1. For y=2, P2=S2=x∈ℝ: x<2. That is, this set consists of all elements of ℝ below 2. For y=π, P3=Sπ=x∈ℝ: x<π. That is, this set consists of all elements of ℝ below π. In fact, For y=∞, P4=S∞=x∈ℝ: x<∞. That is, this set consists of all elements of ℝ below ∞ which is itself ℝ. All the partitions formed above are subsets of ℝ. That is, P=P1, P2, P3, P4=S0.1, S2, Sπ, S∞ is a partition of A=ℝ. Therefore, yes P=Sy:y∈ℝ and y>0, where Sy=x∈ℝ: x<y is a partition of A=ℝ.