Question

3. Suppose ℕ = {1,2,3, … } is the universal set and 𝐴𝐴 = {𝑥𝑥: 𝑥𝑥 ≤ 6}, 𝐵𝐵 = {𝑥𝑥: 4 ≤ 𝑥𝑥 ≤ 9} and
𝐶𝐶 = {2,3,5,7,8}. Then, find 𝐴𝐴 ∩ (𝐵𝐵 ⊕ 𝐶𝐶).

Answer 1

First, let's break down each set individually:

Set A consists of all numbers less than or equal to 6: 𝐴𝐴 = {1, 2, 3, 4, 5, 6}.

Set B consists of all numbers between 4 and 9 (inclusive): 𝐵𝐵 = {4, 5, 6, 7, 8, 9}.

Set C consists of the numbers 2, 3, 5, 7, and 8: 𝐶𝐶 = {2, 3, 5, 7, 8}.

Next, let's find the symmetric difference (⊕) between sets B and C. The symmetric difference of two sets is the set of elements that are in either of the sets, but not in the intersection of the two sets.

The intersection of sets B and C is {5, 7, 8}. Therefore, the symmetric difference of sets B and C is {(4, 6, 9}.

Finally, let's find the intersection of set A and the symmetric difference of sets B and C.

𝐴𝐴 ∩ (𝐵𝐵 ⊕ 𝐶𝐶) = {1, 2, 3, 4, 5, 6} ∩ {4, 6, 9} = {4, 6}

Therefore, 𝐴𝐴 ∩ (𝐵𝐵 ⊕ 𝐶𝐶) = {4, 6}.