Consider the following: 1. A\cap B=A\cap C\Rightarrow B=C 2. A\cup B=A\cup C\Rightarrow B=C Which of the above is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 ✓
Correct Answer: D. Neither 1 nor 2
Explanation
Neither statement is universally true because cancellation laws do not hold for arbitrary sets in union or intersection alone. For instance, if A = \{1, 2\}, B = \{1\}, and C = \{1, 3\}, A \cap B = A \cap C = \{1\} but B \neq C. Both statements are incorrect.
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?