U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}.Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).)a.x ∈ {1}.b.x ∈ ⊘.c.x ∈ {1, 2}.d.x ∈ B and x ∈ C.
Question
U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}.Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).)a.x ∈ {1}.b.x ∈ ⊘.c.x ∈ {1, 2}.d.x ∈ B and x ∈ C.
Solution
First, let's determine what B U C is. The union of two sets is a set of all distinct elements from both sets. So, B U C = {{1}, {1, 2}, 2, {2}}.
Next, let's determine what U - (B U C) is. The difference of two sets is a set of elements that exist in the first set but not in the second set. So, U - (B U C) = {1, 2, {1}}.
Now, let's look at the options:
a. x ∈ {1}. This could be true if x = 1.
b. x ∈ ⊘. This is not true because U - (B U C) is not an empty set.
c. x ∈ {1, 2}. This could be true if x = 1 or x = 2.
d. x ∈ B and x ∈ C. This is not true because if x ∈ B U C, then x cannot be in U - (B U C).
So, the valid statements are a and c.
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