Match List - I with List - II. Suppose A, B and C are three non-empty sets. Choose the correct answer from the options given below :List - I List - II A. De-Morgan's Law I. $A \setminus B = A \cap B^C$ B. Associative Law II. $(A \cup B)^C = A^C \cap B^C$ C. Distributive Law III. $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ D. Difference of sets Law IV. $(A \cup B) \cup C = A \cup (B \cup C)$
The question requires matching the names of set theory laws with their corresponding mathematical expressions.
Matching Set Theory Laws
A. De-Morgan's Law
De-Morgan's Laws describe the relationship between complements and unions/intersections. One form states that the complement of a union is the intersection of the complements: $(A \cup B)^C = A^C \cap B^C$ This matches expression II in List - II.
B. Associative Law
The Associative Law applies to operations like union and intersection, indicating that the grouping of elements does not affect the outcome. For the union operation: $(A \cup B) \cup C = A \cup (B \cup C)$ This matches expression IV in List - II.
C. Distributive Law
The Distributive Law shows how one set operation distributes over another. For the union distributing over intersection: $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ This matches expression III in List - II.
D. Difference of Sets Law
The difference of two sets, $A \setminus B$, consists of elements that are in set A but not in set B. This can be expressed using intersection and complement: $A \setminus B = A \cap B^C$ This matches expression I in List - II.
Summary of Matches
Based on the definitions:
- A corresponds to II (De-Morgan's Law)
- B corresponds to IV (Associative Law)
- C corresponds to III (Distributive Law)
- D corresponds to I (Difference of sets Law)
Therefore, the correct combination is A-II, B-IV, C-III, D-I.
Similar Questions
Match List - I with List - II.
List - I List - II A. Domain of function $f(x) = \frac{1}{\sqrt{x^2 - 1}}$ I. $[2, \infty)$ B. Range of function $f(x) = \frac{1}{\sqrt{x^2 - 1}}$ II. $(-\infty, -1) \cup (1, \infty)$ C. Domain of function $f(x) = \sqrt{x - 2}$ III. $(0, \infty)$ D. Range of function $f(x) = \sqrt{x - 2}$ IV. $[0, \infty)$ Choose the correct answer from the options given below :
Match List - I with List - II on the basis of relationship.
List - I List - II A. Complement operation I. all possible subsets B. Power set operation II. tuples (ordered) C. Cartesian product III. universal set D. Union and intersection IV. difference (symmetric) Choose the correct answer from the options given below :
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- When a Coin is tossed twice which of the following is the probability of getting both tails ?
- When a dice of six faces {1, 2, 3, 4, 5, 6} is thrown, which of the following is the probability of getting even number ?
- Which of the following in the variance of the data ?
6, 8, 10, 12, 14, 16, 18, 20, 22, 24 - For the given dataset :
$\begin{array}{cc} x & f(x) \\ \hline 2 & 1/4 \\ 3 & 1/2 \\ 4 & 1/4 \end{array}$
Which of the following is the expected value of $x$ ? - When a Coin having head and tail is thrown, which of the following is probability of not getting head ?
- The standard deviation for the following data is :
$\begin{array}{|c|c|c|c|c|c|} \hline x_i & 3 & 8 & 13 & 18 & 23 \\ \hline f_i & 7 & 10 & 15 & 10 & 6 \\ \hline \end{array}$ - For two distributions the standard deviations are 21 and 14 respectively and their coefficients of variations are 60 and 70 respectively. Which of the following is correct for their arithmetic means ?
Important Questions from Mixed Topic (CUET PG)
- Who was the founder of Bolshevik Communist party?
- What is the key guide to statecraft in the realist tradition?
- Chronologically arrange the events in the Cold War period.
A. Berlin Wall is constructed
B. Communist China joins the UN
C. Soviet invasion of Czechoslovakia
D. Berlin Blockade
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A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?
