Question:
For the nonempty sets \( A \) and \( B \), which of the following is NOT true? \( \overline{A} \) is the complement of A
For the nonempty sets \( A \) and \( B \), which of the following is NOT true? \( \overline{A} \) is the complement of A
Show Hint
To validate set identities, simplify the expressions by applying set operations and see if both sides of the equation match.
Updated On: Mar 20, 2026
- \( A \cap (\overline{A} \cup B) = A \cap B \)
- \( A \cup (\overline{A} \cap B) = A \cup B \)
- \( A - (A - B) = B \)
- \( A \cup (B - A) = A \cup B \)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
- Option (3) is incorrect because \( A - (A - B) \) results in \( B \cap A \), not \( B \) directly.
- The other options are valid set identities based on set theory operations.
- The other options are valid set identities based on set theory operations.
Was this answer helpful?
0
0
Top NPAT Quantitative Aptitude Questions
- If \( U = \{ x \ | \ x \in \mathbb{N}, x \leq 10 \} \) is the universal set, and \( A = \{ 1, 3, 5, 7, 9 \} \), \( B = \{ 2, 4, 6, 8, 10 \} \), and \( C = \{ 1, 2, 3, 4 \} \), the number of elements in \( A - (B \cap C) - (B' \cap C') \) where \( B' \) and \( C' \) are the complements of B and C, respectively is:
- A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
- Let \( A = \{ 1, 2, 5 \} \), \( B = \{ 1, 2, 3, 4 \} \), and \( C = \{ 2, 5, 6 \} \) be the three sets. If \( D = [A \times (B \cap C)] \cap [(A - B) \times C] \), then which of the following is true?
- If \( f(x) = \frac{x-1}{x+1} \), then for \( k>0 \), \( f^{-1} \left( \frac{1}{2k+3} \right) = ?
- Which of the following functions satisfies these two criteria: \( f(0) = 0 \) and \( f(x+1) = 2f(x) + 1 \)?
View More Questions
Top NPAT Sets Questions
Top NPAT Questions
- Select the option that best fills in the blank and completes the sentence given below.
\_\_\_\_ our heads are basically similar, differences in size, shape and colour of features produce a variety of appearances. - Select the option that best fills in the blank and completes the sentence given below.
\_\_\_\_ the fact that it was difficult, Dhananjay managed to solve the physics paper. - Select the option that best fills in the blank and completes the sentence given below.
The boys were bored because they had__ to do in the art class. - Select the option that best fills in the blank and completes the sentence given below.
\_\_\_\_ of the actors was paid a hefty amount to perform at the awards function. - Select the option that best gives the meaning of the word/phrase in bold.
Watercolours can be applied undiluted to create a broken-colour effect.
View More Questions