Consider the following statements<br>1. A=(A\cup B)\cup(A-B)<br>2. A\cup(B-A)=(A\cup B)<br>3. B=(A\cup B)-(A-B)<br>Which of the statements given above are correct?
- A. 1 <strong>ONLY</strong>
- B. 2 <strong>ONLY</strong>
- C. 1 and 2
- D. 2 and 3 ✓
Correct Answer: D. 2 and 3
Explanation
Statement 1 evaluates to A \cup B, which is not necessarily A, so it is false. Statement 2: A \cup (B - A) = A \cup (B \cap A') = (A \cup B) \cap (A \cup A') = A \cup B, so it is true. Statement 3: (A \cup B) - (A - B) = (A \cup B) \cap (A \cap B')' = (A \cup B) \cap (A' \cup B) = B \cup (A \cap A') = B, so it is true.
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?