Let A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}. Calculate the value of (A ∪ B) ∩ (A ∪ C).a.{1,2,3}b.{1,2,3,4}c.{1,2,3,4,5}d.{3,4,5}

First, let's understand the symbols used in the question. The symbol '∪' stands for union of sets, which means all the elements that are in either set, or in both. The symbol '∩' stands for intersection of sets, which means all the elements that are common to both sets.

Step 1: Calculate A ∪ B The union of sets A and B, A ∪ B = {1, 2, 3} ∪ {2, 3, 4} = {1, 2, 3, 4}

Step 2: Calculate A ∪ C The union of sets A and C, A ∪ C = {1, 2, 3} ∪ {3, 4, 5} = {1, 2, 3, 4, 5}

Step 3: Calculate (A ∪ B) ∩ (A ∪ C) The intersection of sets (A ∪ B) and (A ∪ C), (A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4} ∩ {1, 2, 3, 4, 5} = {1, 2, 3, 4}

So, the value of (A ∪ B) ∩ (A ∪ C) is {1, 2, 3, 4}, which corresponds to option b.